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RANP'S  SCIENCE  SERIES. 


)     £3-         STOST3 

•         ~'  '"  '&^^^l 

jvE-MAKIN 

MACHINES' 


THF    TH1  ;    •  I'lON    OF   TH  ;:  VART- 

.':•     '  :  '   .M.- 

•J^^l 

A    i-lK  •.  ' 


r.\:    FROM    THE    -'F»:NCH    OF 

M.    LEDOUX. 


tfKUff*- 


D.VA1-    .^TOSTKAND, 

23  MUHVvAY  AND  ^T  WARREN  STREET. 

1879. 


uuivs,E;'srrlf 


ICE-M7OUNG- 

MACHINES: 


THE  THEORY  OF  THE  ACTION  OF  THE  VARI- 
OUS FORMS  OF  COLD-PRODUCING  OR 
SO-CALLED  ICE  MACHINES 

(  MACHINES  A   FROID). 


TRANSLATED  FROM  THE  FRENCH  OF 

M.    LEDOUX, 

Ingenieur  des  Mines* 


REPRINTED    FROM    VAN    NOSTRAND'S    MAGAZINE. 


NEW   YORK: 

D.  VAN  NOSTRAND,  PUBLISHER^ 

23  MURRAY  AND  27  WARREN  STREET. 

1  8  79. 


PREFACE. 


THE  theory  of  Ice-Making  Machines 
has  assumed  a  new  importance,  since  it 
has  been  shown  that  they  may  be  worked 
to  an  economical  advantage  in  some  sec- 
tions, even  where  natural  ice  is  not  diffi- 
cult to  be  obtained. 

But  aside  from  any  question  of  com- 
petition with  natural  ice  in  temperate 
climates,  the  subject  is  of  great  interest 
to  those  who  find  it  desirable  to  produce 
and  maintain  a  low  temperature  in  places 
where  the  requisite  quantity  of  ice  would 
be  too  cumbersome,  and  where  a  refrig- 
erating machine  and  its  driving  power 
can  be  easily  accommodated.  Such  an 
example  is  afforded  by  the  hold  of  a  ves- 
sel sailing  in  a  warm  climate. 

The  conditions  of  effective  working 
of  the  three  classes  of  machines  are 
clearly  set  forth  in  this  little  treatise. 

G.  W.  P. 


ICE-MAKING  MACHINES. 

CHAPTER  I. 

§  1.  IT  has  long  been  known  that  air  is 
heated  or  cooled  when  compressed  or 
dilated. 

The  mechanical  theory  of  heat  defines 
the  conditions  under  which  this  heating 
or  cooling  is  effected,  and  shows  that 
these  effects  are  proportioned  to  the  ex- 
ternal work  performed  by  the  air,  with 
the  restriction  that  in  expanding  the  resist- 
ance overcome  by  the  gas  is  always 
equal  to  the  elastic  force  of  the  latter. 

If  t  and  t'  represent  successive  tempe- 
ratures of  a  unit  weight  of  a  permanent 
gas,  which  has  been  compressed  or  dila- 
ted under  conditions  above  stated  in 
producing  an  amount  of  work  (either  re- 
sistant or  motive)  equal  to  W,  we  shall 
have 


A  being  the  reciprocal  of  the  mechan- 
ical equivalent  of  heat  =^-|^-  and  c  being 
the  specific  heat  of  the  gas  at  constant 
yolume. 

In  a  saturated  vapor  a  part  of  the  ther- 
mal equivalent  of  the  external  work  is 
transformed  into  latent  heat;  the  other 
part  alone  becomes  sensible  under  the 
form  of  external  heat. 

This  is  expressed  in  the  fundamental 
equation 


in  which  cl  is  the  specific  heat  of  the  liq- 
uid, x  the  proportion  of  vapor  in  the 
unit  of  weight  of  mixture  of  liquid  and 
vapor,  p  the  latent  heat  of  the  vapor  and 
W  the  external  work  accomplished. 

We  see  from  these  equations  that  for 
the  same  quantity  of  heat  transformed 
into  work,  the  range  of  temperatures 
must  be  greater  with  a  gas  than  with 
saturated  vapors. 

§  2.  Whether  we  employ  a  permanent 
gas  or  a  vapor,  the  apparatus  designed 
for  the  refrigerating  effects  is  based  upon 
the  following  series  of  operations  : 


Compress  the  gas  or  vapor  by  means 
of  some  external  force,  then  relieve  it  of 
its  heat  so  as  to  diminish  its  volume ;  next, 
cause  this  compressed  gas  or  vapor  to 
expand  so  as  to  produce  mechanical  work 
and  thus  lower  its  temperature.  The 
absorption  of  heat  at  this  stage  by  the 
gas,  in  resuming  its  original  condition, 
constitutes  the  refrigerating  effect  of  the 
apparatus. 

When  the  cooling  takes  place  at  con- 
stant pressure,  the  cycle  of  operations 
can  be  represented  by  the  diagram  Fig.  1 
in  which  the  abscissas  represent  volumes, 
and  the  ordinates  pressures. 

The  gaseous  body  taken  at  the  press- 
ure P0  and  under  the  volume  V0  is  com- 
pressed to  the  tension  Px  and  the  volume 
Vj.  It  is  then  cooled  under  constant 
pressure  so  that  the  volume  Vj  becomes 
V/,  then  it  is  allowed  to  expand,  the 
pressure  Pl  becoming  P0  and  the  volume 
changing  from  V/  toV2.  Finally  it  is 
brought  to  the  original  volume  V0  by 
transferring  heat  to  it  under  constant 
pressure.  The  area  V^jV/V,,  represents 


9 

the  work  expended  and  the  lineV0V2  the 
refrigerating  effect  obtained. 

An  inspection  of  the  figure  shows  that 
a  refrigerating  machine  is  a  heat  engine 
reversed. 

If  instead  of  cooling  the  gas,  to  reduce 
it  from  the  volume  Vx  to  V/,  it  be  heat- 
ed so  as  to  assume  the  volume  V/' 
greater  than  'Vl  an  amount  of  work  is 
obtained  which  is  represented  by  the 
vertically  shaded  area  V^'V/'V^  the 
heat  expended  is  represented  by  the 
length  V^/'. 

It  should  be  noticed  that  in  the  case 
of  a  permanent  gas,  the  changes  from 
volume  V  to  Y/  or  V/'  and  from  V2  or 
V/  to  V0  are  accompanied  by  correspond- 
ing changes  in  temperature.  In  the 
case  of  a  condensable  vapor  these  changes 
are  effected  at  a  constant  temperature, 
the  addition  or  subtraction  of  heat  taking 
effect  in  an  evaporation  of  the  liquid  or 
a  condensation  of  the  vapor. 
/  §  3.  From  this  similarity  between  heat 
motors  and  freezing  machines  it  results 
that  all  the  equations  deduced  from  the 


10 


mechanical  theory  of  heat  to  determine 
the  performance  of  the  first  apply  equally 
to  the  second. 

If  Q,  be  the  quantity  of  heat  taken 
from  or  added  to  a  given  mass,  of  com- 
pressed gas  or  vapor,  and  Q  the  quan- 
tity of  heat  necessary  to  subtract  from 
or  add  to  the  expanded  mass  in  order 
to  bring  it  to  its  initial  state,  T0  and 
Tl  the  absolute  temperatures  correspond- 
ing to  the  volumes  V0  and  Yx  and  W 
the  work,  either  active  or  resistant  devel- 
oped by  the  machine.  The  fundamental 
principle  of  the  mechanical  theory  of 
heat,  if  the  gas  returns  exactly  to  its 
primitive  condition,  affords  the  equation, 

Qi_Q=AW 

If  the  cycle,  of  changes  is  the  so-called 
cycle  of  Carnot;  that  is  to  say,  if  the 
lines  V^,  Y/V2,  and  V/'V/  are  adiaba- 
tic  curves;  then  we  have 

Q=Q.    Q.-Q 

T0     T,     T,-T0 

The  quantity  of  work  developed  by  a 
heat  motor,  under  these  circumstances, 


11 

is  for  each  heat  unit  or  calorie,  whatever 
the  intermediate  agent, 


The  efficiency  depends  upon  the  dif- 
ference between  the  extremes  of  temper- 
ature. 

The   performance   of    a   refrigerating 
machine  depends  upon  the  ratio  between 
the   calories   eliminated    and    the   work 
expended  in  cooling. 
It  is  expressed  by 
Q 
W 
and  we  have 

Q_    AQ  T0 

W-Q,-Q-AT,-T; 

This  result  is  independent  of  the  na- 
ture of  the  body  employed. 

Unlike  the  heat  motors,  the  freezing 
machines  possess  the  greatest  efficiency 
when  the  range  of  temperatures  is  small, 
and  when  the  final  temperature  is  eleva- 
ted. 
y  In  a  freezing  machine  employing  a  va- 


12 

por,  T0  being  the  absolute  minimum  final 
temperature,  this  final  temperature  T2 
in  a  machine  employing  a  permanent  gas 
is  different  from  the  initial  temperature 
T0,  and  we  have, 


We  can  write  for  the  efficiency 
Q  =  A     T2 

Comparing  the  efficiencies  of  the  two 
machines  it  is  evident  that  the  perform- 
ance becomes  less  in  proportion  as  we 
obtain  lower  final  temperatures. 

Theoretically  there  is  no  .advantage  in 
employing  a  gas  rather  than  a  vapor  in 
order  to  produce  cold  even  if  the  com- 
pression be  made  without  addition  or 
subtraction  of  heat. 

The  choice  of  the  intermediate  body 
would  be  determined  by  practical  consid- 
erations based  on  the  physical  character- 
istics of  the  body,  such  as  the  greater  or 
less  facility  for  manipulating  it;  the 
extreme  pressures  required  for  the  best 
effects,  etc. 


13 

Air  offers  the  double  advantage  that 
it  is  everywhere  obtainable,  and  that  we 
can  vary  at  will  the  higher  pressures  in- 
dependent of  the  temperature  of  the 
refrigerant.  But  it  is  cumbersome,  and 
to  produce  a  given  useful  effect  the  appa- 
ratus must  be  of  large  dimensions. 

Liquids  on  the  other  hand  allow  the 
use  of  smaller  machines,  but  are  obtained 
only  at  a  greater  or  less  cost. 

Furthermore  the  maximum  pressure  is 
determined  beforehand  by  the  temperature 
of  the  refrigerant,  and  depending  on  the 
nature  of  the  volatile  liquid;  this  press- 
ure is  often  very  high. 

§  4.  The  foregoing  conclusions  are 
based  on  the  hypothesis  that  the  com- 
pression and  expansion  follow  the  adia- 
batic  lines  V0V1  and  V/Va,  that  is  to  say 
that  the  changes  of  volume  and  pressure 
follow  the  cycle  of  Carnot. 

This  hypothesis  is  realized  when  the 
cooling  is  accomplished  outside  of  the 
compression  cylinder  and  after  the  gas 
has  been  raised  to  the  pressure  P:. 

If  the  cornpresai^EpfcSFSEfeeted  accord- 


OF   THE 


UNIVERSITY 


14 


ing  to  some  cycle  different  from  Car- 
not's,  the  efficiency,  if  it  be  a  heat  motor, 
would  be  diminished,  but  in  a  freezing 
machine  it  would  be  greater  or  less,  de- 
pending upon  the  manner  in  which  the 
successive  operations  were  effected. 

Suppose  for  example  that  instead  of 
cooling,  the  gaseous  body  outside  the 
compression  cylinder,  it  be  done  during 
compression  within  the  cylinder  in  such 
a  manner  as  to  maintain  a  constant 
temperature.  This  hypothesis  would  be 
graphically  represented  in  Fig.  1  by  re- 
placing the  adiabatic  curve  V0Vj  by  the 
isothermic  curve  V0V/.  The  work  of 
resistance  of  the  machine  would  then  be 
represented  by  the  curvilinear  triangle 
VjjVjV/V,,.  The  quantity  of  negative 
heat  produced  represented  by  the  line 
V0V2  remains  the  same.  The  efficiency 
of  the  freezing  machine  would  be  thus 
augmented  as  the  resistant  work  of  the 
motor  would  be  less  than  the  preceding 
case  for  the  same  quantity  of  negative 
heat  produced. 

The    cooling   of   vapors   during    com- 


15 

pression  is  not  readily  realized,  since  it 
is  effected  at  a  constant  temperature  and 
one  which  is  lower  than  the  refrigerant. 
It  is  realized  though  somewhat  incom- 
pletely in  the  case  of  permanent  gases 
since  their  temperature  during  compres- 
sion is  above  that  of  the  refrigerant. 

§  5.  The  efficiency  is  calculated  in  the 
following  manner. 

We   suppose   the   compression   to   be 

made  at  a  constant  temperature.     Then 

\  by  Marriotte's  Law  we  have  P^^P^. 

The  work  of  resistance  to  compression 
would  be 

V  V 

PV   7    ° "RT  /    ° 

r  —  -^oV^y"  —  •tt-Vy' 

and  we  shall  have  as  in  the  preceding 
case. 

AWr  =  Q, 

R  is  a  constant,  uniform  for  the  air  at 
29.27  inches  and  a  unit  of  weight  is  sup- 
posed taken. 

The  gas  dilating  from  the  temperature 
T0  to  T2  without  gaining  or  losing  heat, 
we  shall  have  for  the  work  of  dilatation, 


16 

inclusive  of  the  work   at  full   pressure 
during  introduction  ; 


The  performance  is  represented  by 


and  we  have 


A    Q- 

Q.-Q 


*c(T.-T.) 


We  have  also 

c       E 


Jc  is  the  ratio  of  specific  heat  at  constant 
pressure  to  the  specific  heat  at  constant 
volume;  this  ratio  is   =1.41  and  is  the 
same  for  all  permanent  gases. 
It  follows  then 

Qm         nn 

A                         A  •••« — A« 
rrrA  /    

If  the  compression  follows  an  adiabatic 
curve,  we  shall  have  for  the  efficiency — 


17 

calling  Tx  the  absolute  final  temperature 
of  the  compression 

O  T  — T 

A         *v        A  o  2 


Q-Q~     T,-T0-(T0-T2) 

- 

It  is  easyftto  show  that 


k— I 

Ztfr-i 


is  greater  than 


k      OPO 

and  consequently  that  the  efficiency  in 
the  first  case  is  less  than  in  the  second. 

The  employment  of  air  presents  a  cer- 
tain theoretical  advantage  over  volatile 
liquids,  inasmuch  as  it  admits  of  cooling 
to  a  certain  extent  during  compression. 

We  will  now  examine  in  succession 
some  of  the  recently  invented  freezing 
machines  (machines  a  froid).  The  Air 
Machine  of  M.  Giffard;  the  Sulphurous 
Acid  Machine  of  M.  Pictet,  and  the  Am- 
monia Machine  of  M.  Carre. 


18 

CHAPTER   II. 
GIFFARD'S  AIR  MACHINE. 

§  7.  This  machine  consists  of  a  single- 
acting  cylinder  A,  the  piston  of  which  is 
furnished  with  two  valves  opening  from 
without  inward.  This  cylinder  is  sur- 
rounded with  a  jacket  leaving  a  space 
within  which  circulates  a  current  of  cold 
water. 

There  is  a  second  cylinder,  B,  also 
single-acting,  and  having  a  solid  piston, 
and  with  a  diameter  a  little  smaller  than 
the  first.  At  the  bottom  of  this  cylinder 
are  two  openings  closed  by  valves,  open- 
ing, one  outward  and  the  other  inward, 
and  operated  by  levers  which  are  worked 
by  cams  on  the  driving  shaft. 

The  pistons  are  driven  by  crank  con- 
nections with  the  main  shaft. 

The  condenser  B  is  a  surface  condenser 
and  receives  a  current  of  cold  water  from 
the  envelope  of  the  compressor  cylinder 
A.  A  Keservoir  of  wrought  iron,  B',  is 
connected  with  the  condenser  by  a  tube 
and  communicates  also  with  the  bottom 
of  the  expansion  cylinder  B. 


19 


20 

§  8.  The  air  taken  in  at  ordinary  press- 
ure is  compressed  in  the  cylinder  A  till 
it  has  the  density  of  that  in  the  reservoir ; 
it  is  then  allowed  to  flow  into  the  con- 
denser B  and  the  reservoir  B'.  During 
this  passage  it  loses  a  great  part  of  the 
sensible  heat  which  it  attains  during 
compression,  and  is  brought  nearly  to  the 
temperature  of  the  surrounding  air. 

During  this  time  the  valve  s  of  the 
cylinder  B  opens  and  permits  a  certain 
amount  of  air  equal  in  weight,  to  that 
which  is  expelled  from  A,  to  pass  from 
the  reservoir  into  the  cylinder  producing 
a  certain  amount  of  work.  Then  the 
valve  s  closes, — the  air  in  the  cylinder  B 
expands  producing  again  work  which  may 
be  deducted  from  the  work  of  compression 
and  the  temperature  is  lowered.  When 
the  piston  B  reaches  the  upper  limit  of 
its  stroke,  the  valve  s'  opens  and  the 
cooled  air  as  the  piston  descends  escapes 
by  the  tube  T. 

The  cooling  experienced  by  the  air, 
during  compression,  by  contact  with  the 
cooled  sides  of  the  cylinder  is  scarcely 
sensible. 


21 

The  machine  therefore  acts  under  con- 
ditions set  forth  in  §  2  and  we  know  that 
its  useful  effect  cannot  exceed  the  value 

T  T 

Apir-^V     or     A,,      ' 


m          VJ-         **m  m 

i       -*-o  Ai       "*•« 

By  means  of  the  adjustable  cams  we 
can  regulate  at  will  the  action  of  the 
valves  s  and  s'.  If  we  shorten  the  time 
of  admission  into  the  cylinder  B,  the 
pressure  will  increase  in  the  reservoir; 
for  the  amount  flowing  into  B  should  be 
equal  to  that  forced  into  the  reservoir 
from  A.  The  temperature  of  the  air  ex- 
pelled will  then  be  less.  If,  on  the  con- 
trary, we  increase  the  time  of  admission 
the  reservoir  pressure  will  diminish,  and 
the  temperature  of  outflowing  air  will  be 
increased. 

The  apparatus  presents  then  this  im- 
portant peculiarity — that  we  can  vary  the 
useful  effect  of  the  machine  at  will, 
through  wide  limits. 

As  the  air  leaves  B,  at  the  pressure  of 
the  atmosphere,  the  minimum  limit  of 
pressure  is  established,  below  which  the 


22 

expansion  cannot  be  pushed,  and  which 
is  controlled  by  the  relative  dimensions 
of  the  two  cylinders. 

We  will  proceed  to  calculate  the  cool- 
ing effect  produced  by  this  machine  and 
the  corresponding  work  required.  We 
shall  neglect  at  first  the  effect  of  waste 
spaces  in  the  machine,  and  of  watery 
vapor  in  the  air. 

§  9.  JLet  P0,  t0  and  T0  be  the  pressure  and 
temperature  (counted  from 
absolute  zero)  of  the  air. 

V0  the  volume  described  by  the 
piston  A. 

Vx  the  volume  of  air  when  at 
pressure  Pr 

Vj  is  then  the  volume  described 
by  the  piston  during  the  out- 
flow. 

m= weight  of  air  whose  volume 
passes  from  Y0  to  Vj. 

Pl9  ^  and  Tj  the  pressure  and 
temperature  of  compressed 
air  delivered  from  A. 

Y  '  t '  and  T  '  the  volume  and 


23 

temperature  after  passing  into 
the  condenser. 
V2  the  total  volume   described 

by  piston  B. 

P2,  Z2  and  T2  the  pressure  and 
temperature  of  the  air  at  the 
end  of  the  course  of  this 
piston. 

During  compression  the  cooling  by 
simple  contact  with  the  sides  of  the  cylin- 
der is  insignificant.  We  shall  neglect 
this  and  also  assume  that  no  heat  is  receiv- 
ed from  the  sides  of  the  cylinder  B. 

FIKST     PEKIOD I      COMPRESSION. 

.- 

§  10.  When  air  is  compressed  without 
losing  or  gaining  heat,  the  pressure  and 
temperature  at  each  instant  bear  the  re- 
lation to  each  other  expressed  by  the 
equation 

PoVo*  =  p^t  (1) 

in  which  k  is  the  ratio  of  specific  heat  of 
constant  pressure  to  the  specific  heat  of 
constant  volume. 

0.23751 

~ 


24 

Gay  Lussac's  law  affords, 

P0V0=BmT0  (2) 

and  P1V1=EmT1  (3) 

From  equations  1  2  and  3  we  deduce 


k— 1 

(6) 

The  work  of  the  resistance  to  compression 
and  outflow  is 

W'  -  ^i(p1Vi-poVo)-  (6) 

We  have  elsewhere 

k         kc 

c  being  the  specific  heat  of  air  of  con- 
stant volume. 
Equation  (6)  then  becomes 


W,  =(T,-T.).  (7) 

SECOND     PEEIOD :     COOLING. 

The   air  is  cooled  in  the   condenser 
under  constant  pressure.  \  The   volume 


25 

changes  from  Vt  to  V/,  and  the  temper- 
ature from  t.  to  t'. 

T  ' 
we  have;  V/=V-^-  (8) 

and  the  quantity  of  heat  imparted  to  the 
water  of  the  condenser  is  ; 

Q^m&KT.-T/)  (9) 

If  T^T.thenB^AWr 

THIRD   PERIOD;   EXPANSION. 

The  volume  V/  of  air  enters  the  cylin- 

der B  yielding  an  amount  of  work  equal 

to  PjV/.    It  expands  from  V/  to  V2  with- 

out gain  or  loss  of  heat.     We  have  then: 


(11) 
(12) 

k—  1 

whence  T^T/"^'        (13) 


The  work  performed  by  the  air  is 
' 


Wm=(Tl'-T2)  (15) 


26 


The  resistances  to  be  overcome  by  exter- 
nal force  amount  to 


If  the  machine  works  properly,  the  final 
pressure  P2  should  be  equal  to  the  at- 
mospheric pressure. 

The  equations  (10)  (12)  and  (13)  give 

V        V 

__L  —       o 

V  '  ~~  V 
v       T' 

V*  __    ILL 

V0  -  T, 

T        T 

and  ±  -  f=*  (18) 

•*-!  Al 

Equation  (17)  expresses  the  ratio  which 
should  exist  between  the  volumes  of  the 
two  cylinders,  in  order  that  the  air  be  finally 
expelled  at  atmospheric  pressure,  after 
having  been  compressed  by  a  force  P,. 

The  negative  heat  (cooling),  produced 
by  the  apparatus,  is  the  quantity  of 
heat  necessary  to  restore  the  air  from 
the  temperature  Z2  to  the  temperature  to9 
under  constant  pressure. 


27 
Q=™*c-(T0-T2) 

OT  m*vWl_TA     I"  (19) 


§  11.  Since  a  given  weight  of  air  is  re 
stored,  at  the  end  of  the  operation,  to  the 
same  temperature  and  pressure  it  had  at 
the  beginning  it  follows,  that  it  has  been 
through  a  perfect  cycle  and  we  have  from 
the  mechanical  theory  of  heat; 


The   theoretical  performance   of    the 
machine  is,  calling  it '«, 

Q         =  T0-T2 

" —  •"••  m         m/ 


T,-T,  - 

and  as  we  have  from  equation  (18) 

m   rrv  m  m/ 

rp         rp  rr\  rp 

we  get  finally 

u=-A.  - — °-  -  =A — ^—2 — ,     (20) 

a  result  already  found  in  §  3  by  suppos- 


28 


ing  T/=T0.  If  TX>T0  the  useful  effect 
is  diminished. 

The  efficiency  of  the  machine  will  be 
all  the  greater  as  Ta  approaches  in  value 
to  T0 ;  that  is  to  say  as  it  is  urged  at  a 
lower  pressure  into  the  reservoir.  But 
as  we  lower  the  pressure  of  working,  the 
quantity  of  negative  heat  produced  dim- 
inishes also  and  becomes  nothing  when 
T/=T,. 

The  necessary  driving  power  Wr— Wm 
which  we  proceed  to  calculate,  should  be 
augmented  by  the  passive  resistances. 

If  we  consider  the  refrigerating  ma- 
chine as  composed  of  two  distinct  ma- 
chines driven  by  the  same  shaft,  we  are 
led  to  consider  that  the  work  of  the  pass- 
ive resistances  is  proportional  not  to  the 
final  work  Wr— Wm  but  rather  to  the 
sum  of  the  work  developed  in  the  two 
cylinders  Wr  +  Wm.  Considering  the 
simplicity  of  the  machine,  the  small 
amount  of  friction,  and  the  absence  of  a 
stuffing  box,  we  can  admit  that  the  work 
of  the  passive  resistances  should  not  ex- 
ceed eight  per  cent  of  the  above  total 
work. 


29 

The  resistance  of  the  machine  is  then 


The  following  table  gives  the  amount 
of  refrigeration  obtained,  and  the  work 
expended,  by  passing  a  cubic  meter  of 
dry  air  through  the  machine;  the  press- 
ures in  the  reservoir  varying  from  1£  to 
4£  atmospheres.  The  temperature  of  the 
external  air  is  taken  at  15°  ;  the  temper- 
ature of  the  air  leaving  the  condenser  at 
18°;  temperature  of  the  water  about  13° 
V0=l,  T0  =  288  and  w  =  l*.266. 

§  12.  An  examination  of  the  table  shows 
the  enormous  influence  that  the  passive 
resistances  exert  upon  the  efficiency  of 
air  machines.  It  is  one  of  the  conse- 
quences of  the  inherent  cumbrousness 
which  follows  from  the  use  of  this  body 
in  a  thermic  machine. 

The  useful  effect  produced  is  not  in- 
creased in  proportion  to  the  increase  of 
pressure.  It  is  of  no  advantage  to  em- 
ploy pressures  higher  than  about  4J  at- 
mospheres. Aside  from  the  diminution 
of  efficiency  of  the  air  at  high  pressures, 
a  loss  is  occasioned  by  heat  developed  in 


30 


ped. 


dev 


ori 


gat 


No. 


•jnoq  jad 
jaAiod  asjoq  jaj 


•jnoq  jad 

19AiOd  OSJOq  19  J 


i«  oo  S  S  8 

T—  1O  O^  -H  O 
CQ  rH  -i—  I  rH  i—l 


00 


O  0  0  OOO  O 


'i  O5  GO  GO  O  Oi 


c-i  o  t>  io  i>  to  co 

GO  tO  ^  CO  CO  i>  CO 

r-HGOOt^OlO^t1"^1 

cSr-i-rHOOOOO 
OC:OOOOOO 


'papuadxa 


10^  CO^  rH^  CO^  05  O^  O 

J>  GO  O5  TH  O5  O  O5 
O  "^  O5  -rfi  J>  O  O5 

TH  05  CO  1O*  O  GO  O5 


CO  CO  iO  O 


H  1O  to  i>  ->»  GO 
5  i— I  1O  1O  CO  J> 
3  1O  10  O  J>  £> 

rH  O5  CO  ^  1O  O 


T 

IO  GO  i—  i  1O  tO  C 
^  CO  10  10  0  J 


•paure^qo 


uorinuiraiQ; 


•jive 

jo  9in:p3.i9din9j, 


rH  TH  GQ  «  3Q  04 


Q^COrHOlOGOlOO 
^O5  1O  CO  i>  GO  O5  O 


JH^H  10  05  C5  O  GO  10 
POiH  CO  ^  O  t>  i>  GO 

-=      1   1   1   1   1   1 


•noissaidraoo  iQiye 
JIB  jo 


ofio  i>  o  O5  -^H  to  *>• 

T3  rHrHrH  rHr-l 


\<M   \N 

T-N    rH\ 

rH  05  C7  00  CO  ^  ^ 


\O5 

r-i\ 


31 

the  compressor,  and  which  extends  to 
other  working  parts  of  the  machine.  We 
have  said  above  that,  with  a  given  ma- 
chine we  can  vary  at  will  the  pressure  Pl 
by  varying  the  length  of  time  of  the 
opening  of  the  admission  valve  in  the 
cylinder  B.  If  the  time  be  shortened 
the  pressure  and  the  cooling  effect  are 
both  increased;  and  if  the  time  be  in- 
creased P,  is  diminished.  It  is  necessary 
that  we  should  vary  at  the  same  time  the 
working  of  the  emission  valve,  so  that  it 
opens  at  the  moment  when  the  piston 
shall  have  passed  through  a  space  equal 

T  ' 

toVo7=f-corresponding  to  the  atmospheric 

*i 

pressure  on  the  inside  of  the  expansion 

cylinder. 

A  machine  whose  dimensions  and  veloc- 
ity are  such  that  it  uses  1000  cubic  meters 
of  air  per  hour  will  produce  from  8.548 
to  29.375  negative  calories  and  upwards 
per  hour,  provided  that  the  driving 
power  varies  from  4  to  34  horse  power. 

Practically  however  the  efficiency  of 
air  machines  is  not  so  great  as  is  indica 


32 

ted  by  the  above  table  as  no  account  has 
yet  been  taken  of  watery  vapor  in  the  air, 
nor  of  lost  spaces  in  the  machine. 

We  proceed  to  examine  the  influence 
of  these  two  causes  of  loss. 

'  INFLUENCE    OF     MOISTURE    IN     THE    AIR. 

§  13.  This  influence  is  not  to  be  neg- 
lected. The  vapor  contained  in  the  air 
condenses  on  the  sides  of  the  expansion 
cylinder,  and  parts  with  its  latent  heat 
of  vaporization  so  that  the  final  temper- 
ature of  the  air  is  higher  than  it  would 
have  been  if  dry. 

Furthermore  the  snow  produced  from 
this  moisture  accumulates  around  the  ori- 
fice of  the  cold  air  outlet  and  we  cannot 
readily  utilize  the  cold  which  is  required 
to  produce  it.  For  these  two  reasons, 
but  especially  for  the  latter,  the  moisture 
of  the  air  causes  a  notable  loss. 

We  proceed  to  calculate  the  volume 
and  the  temperature  of  the  air  at  the  end 
of  the  expansion  under  the  supposition 
of  a  known  hygrometric  state  of  the  at- 
mosphere, from  which  we  can  easily  de- 


33 

duce  by  the  tables  the  pressure  of  the 
vapor  p0  and  its  weight  /^ 

In  the  compression  cylinder  of  watery 
vapour  not  being  near  the  saturation 
point,  and  exerting  a  feeble  pressure  will 
behave  nearly  as  a  perfect  gas;  its  vol- 
ume and  its  temperature  are  represented 
by  the  relations  pvk=  a  constant,  in  which 


The  total  pressure  of  air  and  vapor 
being  represented  by  P,  the  pressure  of 
the  vapor  being/*,  that  of  the  air  alone  will 
be  P—p  and  we  shall  have  preserving 
our  former  notation: 

P,V*=P.VJ,  (21) 

^,V*=p0V*,  (22) 

(P.-ft)V.=Bf»T.,  (23) 

p0V0=BXT0>  (24) 

(P.-.pJV^BmT,,  (25) 

^V^BXT,.  (26) 

The  work  of  the  resistance  to  compress- 

ionis 


34 


(27) 
or 


c'  is  the   specific  heat  under   constant 
volume  of  the  superheated  vapor 

c'=  0,3407. 
After  cooling  the  volume  becomes 

V'^V,  ^  (28) 

*1 

and  we  have 

^V^RXTV 

From  equations  21  and  22  we  can  de- 
duce the  pressure  in  the  reservoir. 

We  can  determine  by  examining  a 
table  of  tensions  of  saturated  steam 
whether  the  pressure  pl  is  greater  or  less 
than  the  pressure  which  corresponds  to 
the  temperature  T/.  If  it  be  less  the 
air  will  not  be  saturated  with  vapor  when 
leaving  the  condenser,  and  the  heat  ab- 
sorbed by  the  latter  will  be  : 


If  the  pressure  pl  is  greater  than  the 


35 


pressure  />/,  corresponding  to  the  tem- 
perature T/  for  saturated  steam,  there 
will  be  a  condensation  of  some  of  the 
vapor  in  the  condenser ;  the  amount  con- 
densed will  be 

/I.CL-O 

and  the  pressure  of  the  vapor  entering 
into  the  cylinder  B  will  be  p^,  that  of 
the  air  being  Pl—p1f. 
We  shall  have  also : 

aj/=Ai=£i;  PO 

Pi  P.       Pi 

We  see  that  the  quantity  of  vapor  not 
.condensed  by  the  cooling,  and  passing 
into  the  expansion  cylinder,  will  continu- 
ally diminish  in  proportion  as  the  work- 
ing pressure  is  raised.  The  influence  of 
the  humidity  in  the  air  will  therefore  be 
less  as  the  pressure  is  made  greater. 

The  weight  of  the  mixture  of  air  and 
vapor,  which  is  m  -f  /^  if  there  is  no  con- 
densation in  the  cooler  or  m  +  jt^x/  if 
there  is  a  condensation,  is  carried  into 
the  cylinder  B  where  it  encounters  the 
surfaces  cooled  during  the  preceding 


36 

stroke.  We  can  neglect  the  influence  of 
these  cold  surfaces  upon  the  air  alone, 
but  not  upon  the  mixture  of  air  and 
vapor.  The  latter  is  converted  into  frost 
which  releases  a  certain  amount  of  heat 
to  be  imparted  to  the  metal,  and  which 
during  the  expansion  is  restored  to  the 
air. 

Suppose  at  first  that  there  is  no  con- 
densation in  the  cooler,  there  is  conveyed 
to  the  cylinder  a  weight  /^  of  saturated, 
or  nearly  saturated,  vapor  at  the  tem- 
perature Tj'.  We  may  assume,  consider- 
ing the  very  low  temperature  of  the  sur- 
faces, that  all  the  vapor  is  condensed 
here ;  it  will  disengage  a  quantity  of  heat 
C,  which  is  approximately  equal  to 
/^(r/4-79).  r/  being  the  latent  heat  of 
the  vapor  corresponding  to  the  tempera- 
ture £/,  79  is  the  latent  heat  of  water 
released  on  freezing. 

The  heat  C  is  gradually  restored  to  the 
air  during  expansion. 

The  pressure  of  the  air  becomes  P1? 
and  the  volume  introduced  into  the  cyl- 
inder is 


V'= 


37 
R»tT.' 


The  differential  equation  of  the  work  is 

CTmdT  +  ^/vn?-^= 
A  A  A 


Cj  being  the  specific  heat  of  ice,  =0,5 
c  c,       \dT       dC  d 

"^"      2 


We  do  not  know  the  law  of  relation 
between  C  and  T1?  that  is,  how  to  com- 
municate to  the  air  the  heat  released  from 
the  water  and  ice  formed.  We  are  forced 
to  make  a  hypothesis  which  is  not  rigor- 
ously exact,  but  which  is  sufficiently  ap- 
proximate. 

We  will  suppose  that  the  transmission 
is  proportioned  to  the  fall  of  tempera- 
ture, and  therefore  that 


in  which 

_«•/+  79 

Y  —  iji  '__rp 

whence  we  have; 


38 

i  dT  d'V 


integrating  we  get 


AEV          ~™      r~T,  ~     V," 

,  /v^+^n/r',  _  vs 

-~-^( 


we  have  furthermore 
PoV2  = 


whence  T\  _  P.Y/7 

T    ~~  P  V  ' 

*••  -1-  0  *  2 

Equation  29  can  then  be  written ; 


We  can  obtain  the  value  of  T2  by  suc- 
cessive approximations. 

An  approximate  value  for  T2  is  found 
to  be 


39 


Suppose  now  that  condensation  occurs 
in  the  cooler,  we  find  by  the  tables  the 
pressure  of  pf  of  saturated  vapor  of 
temperature  T/.  and  we  can  deduce  the 
weight  of  the  vapor  condensed  in  the 
cooler. 

We  shall  have  then; 


r=*: 

-1-]  "•"  J-a 

The  equations  29  and  30  apply  in  this 
case  as  in  the  preceding. 

The   quantity  of   disposable  negative 
heat  is  ; 

Q=m*c(T.-Tf)  (31) 

since  we  suppose  the  negative  heat  of  the 
snow  formed  to  be  lost. 

Finally  the  work    produced    by    the 
expansion  is  ; 


(T'.-TJ-P.V,     (32) 

or     Wm=  .  +  r)(T/_Ta)    (38) 

A. 

If  there  is  a  condensation  in  the  cooler, 


40 

we  should  replace  jul  in  equations  32  and 
33  by  ^  a?/. 

§  14.  The  following  table  gives  the 
cooling  and  general  effect  obtained  from 
a  cubic  meter  of  air  supposing  a  hygro- 
metric  state  of  ^  and  a  temperature  of  15°. 
The  weight  of  the  air  is  then  1.*  2157 
instead  of  1.*  226  which  is  the  weight  of 
dry  air  at  this  temperature. 

We  have  also  p0=85.k  8  and  //,= 
0.*  00626. 


41 


uoisa-edxa 
ojm  paiireo 
jo 


ori 


negat 
obtai 


No. 


5  CD  O5  CO 

oo  CQ  co 


.  1C  CO  O  1C  GQ 


. 


•jnoq  jad        | 


TH  CO  O  iO  TH  i 


•papuadxa 


i-H  Oi  CO  "^  O  O  ^ 

<^i  co  ic  co  06  as 


Ci  1C  CO  GO  Ci  J>  TH 

GQ  CQ  O)  ^H  1C  CO  t> 

iH  CO*  CO  ^  1C  CO 


J>10OCO 
5  Oi  O5  TH  CQ 


•pam^qo  Suijooo 


pajpdxa  jo 


JH  O"r-Tl>  cTTH"o'100" 
bC       CQ  CO  1C  CO  J>  J> 

RIMINI 


Mossaidraoo 

Ul 


ainssajj 


rH  W  <M  CO  CO  ^  Tj< 


42 

In  comparing  this  table  with  the  table 
of  §  11  we  see  that  the  influence  of  the 
humidity  of  the  air  upon  the  results 
obtained  is  the  greater  when  the  press- 
ure is  low.  We  have  made  a  similar 
remark  in  reference  to  the  passive  resist  - 
ances.  The  theoretical  advantage  there- 
fore of  low  pressures  is  practically  much 
diminished  by  these  causes  of  loss. 

It  is  possible  to  neutralize  almost  com- 
pletely the  influence  of  moisture  in  the 
air.  To  accomplish  this  it  would  suffice 
to  employ  the  air  after  it  had  produced 
its  cooling  effect  and  had  parted  with  its 
moisture.  It  would  be  necessary  to 
make  the  refrigerating  machine  a  closed 
machine,  making  the  same  quantity  of 
air  serve  indefinitely.  The  cooling 
would  be  produced  by  causing  the 
cooled  air  to  pass  through  an  apparatus 
surrounded  by  some  liquid  not  easily 
frozen,  such  as  a  solution  of  calcium  or 
magnesium  chloride.  A  part  of  the  neg- 
ative calories  would  thus  be  used,  as  well 
as  by  direct  contact,  and  so  many  as  are 
not  used  would  not  be  lost,  as  the  air 


43 


passes  directly  to  the  compressor  A,  not 
at  15°  as  before,  but  a-8°  or-10°  of 
temperature.  We  think  that  it  is  only  in 
this  way  that  we  can  improve  the  air 
machine  so  that  it  can  compare  favorably 
with  the  machines  using  a  liquefrable 
gas. 

INFLUENCE    OF    WASTE    SPACES. 

§  15.  We  will  suppose  the  air  to  be 
dry  in  order  to  avoid  complexity  in  our 
calculations. 

Preserving  our  previous  notation  and 
calling  v  the  amount  of  useless  space  in 
the  compression  cylinder,  and  v'  that  of 
the  expansion  cylinder;  /*  the  weight  of 
air  enclosed  in  the  space  v  at  the  end  of 
the  compression,  we  have; 

(34) 
(35) 
(36) 
(37) 

m  being  the  weight  of  dry  air  driven  out 
of  the  compressor. 

Equations  (34),  (35),  (36)  and  (37)  give 
by  elimination  of  }JL 


44 


k-l 

and  T,=T.*  (39) 


The  work  of  resistance  to  compression, 
taking  account  of  the  work  restored  to 
the  piston  as  it  begins  to  ascend,  by  the 
air  in  the  waste  space,  expanding  from 
P^oP,,  is; 


For  the  cooling  period; 

V/^V^'1  (41) 

and  PJ'^EmT/  (42) 

The  heat  Qa  absorbed  by  the  water  of 
the  condenser  is; 

Q^m^T^T/)  (43) 

PERIOD  or  EXPANSION.  —  The  air  coming 

from  the  reservoir  B/  under  pressure  Px 

and  the  temperature  P/,  should  at  the 

moment  of   opening  of   the  inlet   valve 


45 

cause  the  air  in  the  waste  space  and 
whose  volume  is  vf,  to  change  its  press- 
ure from  P0  to  Pj.  This  influences  the 
temperature  T/'  of  the  mixture,  also  the 
weight  m!  of  the  air  which  passes  from 
the  reservoir  into  the  waste  space. 

The  dimensions  of  the  reservoir  being 
very  large  in  comparison  to  the  waste 
spaces,  we  may  assume  that  no  change 
occurs  either  in  temperature  or  pressure 
of  the  reservoir,  while  the  waste  spaces 
are  filled  with  air  at  the  pressure  Pr 

Calling  fjf  the  weight  of  the  air  en- 
closed in  the  waste  space  at  the  moment 
that  the  inlet  valve  opens.  We  have  ; 

PX=K/T2;  (44) 

T2  being  the  final  temperature  of  the 
expanded  air. 

The  stored  up  work  of  this  air  is  ; 


The  weight  mf  of  air  filling  the  waste 
space,  and  having  a  temperature  T/  and 
a  pressure  P}  has  a  stored  energy  of 


46 

After  the  waste  space  is  filled,  the 
stored  up  energy  of  the  total  quantity  of 
air  m!  -f/i'  contained  there  is 

-£-(»»'  H-y^T," 

and  we  have  furthermore; 

PX=B(m'  +  //)T/'.  (45) 

As  we  suppose  there  is  neither  loss  nor 
gain  of  heat  from  the  exterior,  the  differ- 
ence between  the  stored  energy  of  the 
mixture  after  the  mass  in'  is  introduced, 
and  the  sum  of  the  stored  energies  of 
the  masses  m!  and  //  before  mixing  is 
equal  to  the  external  work  performed. 

This  exterior  work  is  evidently  Px  v/, 
and  calling  the  volume  of  mf  before  its 
introduction  into  the  cylinder  under 
pressure  Px  and  temperature  T/  equal  to 
t?/,  then; 


We  have  also 


47 

-p 

Eeplacing  T  by   — 1  and  combining  with 

A.          n  —  1 

equations  44  and  45 

_(P,-P0K 


and    T,=*'»'T    +  XT 


(47) 
or 


When  the  inlet  valve  closes,  the  piston 
has  described  a  volume  V/',  which  has 
been  filled  by  the  weight  m"  of  air  at 
pressure  P:  and  temperature  T/.  We 
have  then; 


There  is  no  external  work  performed 
upon  the  total  mass  of  air,  since  the 
negative  work  of  the  piston  PjV/'  is 
exactly  equal  to  the  positive  work  ex- 
erted by  the  air  of  the  reservoir.  The 
weights  and  temperatures  of  the  air  at 
the  beginning  and  the  end  of  the  intro- 
duction possess  the  following  relations  : 


48 

c 


T/"  being  the  temperature  at  the  end  of 
the  introduction. 
This  equation  gives; 


iji  ///_.  w 

m  -f  }A' 

or         P^Vj'  +  t/) (Pj-P0)v' 

T  '"=  —     - - ! °—  T  >T 

•  "P  "V  TT  _i_  "P  />i"T^  '  i      2 

(48) 
we  also  have 


or 


-^-1*^'5  (49) 

V/  is  given  equations  38  and  41.     Equa- 
tion 49  gives  the  value  of  V/'. 

The  inlet  valve  being  closed,  the  mass 
of  air  m  +  jj.  which  is  at  pressure  Pl  and 
temperature  T/"  expands  without  gain 
or  loss  of  heat  since  we  neglect  the 


49 

influence  of  the  sides  of  the  cylinder. 
At  the  end  of  the  stroke,  this  volume 
becomes  V2  +  v',  its  temperature  T2  and 
its  pressure  P2.  We  have  then 


or 


and 

Equations  50  and  51  give  Y2  and  T2  if 
P2  be  known,  or  P2  and  T2  if  Y2  is 
known  ;  this  latter  being  the  volume  de- 
scribed by  the  piston  of  cylinder  B. 

We  have 

k-l 

T.=T">/ 


VP, 

When  there  is  no  waste  space  we  have 

T2=- 

As  T/"  is  greater  than  T/,  it  results 
that  for  a  given  weight  of  air  passed 
through  the  machine,  at  a  given  working 


50 

pressure,  that  the  final  temperature  of 
the  expanded  air  would  be  higher,  and 
consequently  the  number  of  negative 
calories  produced  would  be  less  than  if 
there  had  been  no  waste  spaces. 
The  work  is  equal  to : 

W^^P^'-P^)  +  (P2-P0)V2 

+  ^l  (P.-PJ»'  (52) 

§  16.  In  order  that  the  machine  should 
work  to  the  best  advantage  it  is  evident- 
ly necessary  that  the  air  should  leave  the 
cylinder  at  atmospheric  pressure,  that  is, 
that  P2  should  equal  to  P0.  There  ought 
then  to  exist  a  certain  relation  between 
the  volume  of  the  compression  cylinder 
V0  +  v,  the  pressure  in  the  reservoir  Pa 
and  the  volume  of  the  expansion  cylinder 
V2  +  v'  which  may  be  determined  by  the 
above  equations.  To  fix  the  dimensions 
of  a  machine  we  may  assume  V0  +  v  and 
P1  as  given,  and  then  deduce  the  value 
ofVf  +  t>'. 

If  we  make  P^Pj  equations  50  and 
51  will  become 


51 


and  P0Va=BmT2, 

whence  fc_i 


/T/    _1P,-P.      V    \ 

VF-jfe-pT  v^r; 


The  work  is 


or 


(54) 


This  value  for  the  work  is  the  same  as 
found  in  §  7,  where  no  waste  space  was 
allowed  for ;  only  the  final  temperature 
T2  being  greater  for  the  same  weight  and 
pressure,  the  work  of  the  air  is  less. 

The  work  of  the  resistance  of  the 
machine  is  then : 

^ffull^s 

^V        OF   THE          n'        \ 

(UNIVERSITY) 

felFOE^^ 


-W-         [!>,-»,') 


_TT      _TT       mkc 

or    Wr-Wm=-£- 

(T.-T.'-T. 
The  negative  heat  produced  is 

Q=fn*e(T.-T,)  (56) 

Q,-Q=Wr-Wm  (57) 

The  performance  of  the  machine  is 
T  —  T 


u— 


_    _  _ 

T.-T/-T. 


or  T.-T.'       _  (58) 

rn  _  m  ttr-L-\       -^o 
xi       *i 

As  T/"  is  greater  than  T1?  the  useful 
effect  is  less  than  if  there  had  been  no 
waste  space. 

§  17.  The  following  table  exhibits  the 
results  of  a  machine  having  waste  space 
of  4  per  cent,  of  the  volume  described  by 
the  pistons.  The  amount  of  air  used 
being  a  cubic  meter  at  15°,  and  weighing 


53 


£ 


bC 


asioq 


"^  IT)  -rH  ?O  O 
-H  00  1-5  CO  O  O 


aArpaga  ja 


unoq  jad 


§  §  §  o  § 


OC5^H  iO  OrHi> 
iO  OO  Oi  1C  t>  CQ  i—  I 

r-  1  o  o  10  os  co  co 
TH  oi  •*  10  o  06  ci 


*5[IOAV 


i>  Ci  ?O  T—  (  1C  J>  C 

^  o  i>  oo  o 


CO  C3  TH  CO  00  GO 

OOQOCOT-HiOO 

^,  «  «  «  «  -^ 

'"*  000 
CQ  CQ  <M 


$  *>  O  t>  CO  1-1  i 


00 


O  t>  CO  i>  CO  TH  J>  00 


TBnn  10 

lowy.  j-v^ 


.. 

^OiOO55OO 

oo  ^  o  o  j>  oo 

I       I      I      I       I      I       I 


•jossajdraoo  uioij 


54 

1*  226.     In  the  cooler  the  air  is  brought 
to  18°. 

By  comparing  these  results  with  those 
of  §  11,  we  see  that  the  effect  of  waste 
spaces  is  by  no  means  to  be  neglected 
since  it  results  in  a  loss  of  about  100 
calories  for  each  theoretic  horse  power 
per  hour. 

§  18.  We  can  neutralize  the  influence 
of  waste  space  by  closing  the  outlet  valve 
of  cylinder  B  before  the  end  of  the 
stroke,  so  as  to  compress  the  air  in  this 
space;  the  stroke  of  the  piston  being 
exactly  determined,  the  air  in  the  waste 
space  may  be  brought  at  the  opening  of 
the  inlet  valve  to  the  temperature  T/ 
and  the  pressure  P/. 

In  this  case  the  equations  34  and  43 
apply  without  change. 

During  the  period  of  expansion  we 
have: 


,  (60) 

P^R/T/ 

whence 


55 


(62} 


The  work  restored  by  piston  B  is  to 
make  allowance  for  the  compression  of 
air  in  the  waste  space  from  the  pressure 
Pn  to  P,  : 


7, 

W—  -— 
m  — 


'—  P  V  ^_ 

Jrav2/ 


—  P 

' 


P 

* 


V  —V 

,./Vo        Vi 


(63) 


or 


T2'  being  the  temperature  of  the  air  in 
the  cylinder  at  the  moment  compression 
commences  before  the  end  of  the  stroke. 
We  have  then  : 


(UNIVERSITY) 
/v 


56 

k_  i 


When  the  machine  is  well  regulated, 
the  final  pressure  P,—  P0  and  the  equa- 
tions 63  and  64  become 

Wm=^r-i(PiV/-p°v=) 

+^ip-"'^    (65) 

WW=^(T/-T,) 

and 


"We  have  also : 

T7      i~7. = T7   /    i    /,./'  V        / 


57 

We  see  that  in  equation  66  the  term 
relating  to  waste  spaces  disappears  if  we 
make  v  =  v'.  The  equation  then  becomes 

Wr  -  W^^CW-V,')  -  P0(V0-V2)] 

The  volume  Va  +  w'  is  determined  by 
means  of  equations  39,  41  and  67  when 
the  pressure  Pl  is  known. 

Keciprocally  when  V0,  v,  V2  and  v'  are 
known  (the  dimensions  of  the  machine) 
then  V/  is  readily  found,  and  conse- 
quently Pt  and  Tj,  the  pressure  and  tem- 
perature at  the  end  of  the  stroke  in  cyl- 
inder B  to  insure  the  escape  of  the  air  at 
the  atmospheric  pressure. 
**  §  19.  It  was  remarked  in  §  5  that  the 
efficiency  of  the  machine  could  be  nota- 
bly improved  by  cooling  the  air  in  the 
interior  of  the  compressor  cylinder. 

This  result  can  be  accomplished,  in 
part  at  least,  if  not  completely,  by  means 
of  a  ject  of  water,  such  as  is  employed  in 
compressed  air  engines. 

We  will  proceed  to  calculate  the  work 
necessary  for  the  compression  in  this 


58 

particular  case,  neglecting  the  effect  of 
waste  spaces. 

Let  m  be  the  weight  of  dry  air  occu- 
pying the  volume  V0.  Let  M  represent 
the  weight  of  water  injected  together 
with  the  amount  of  moisture  in  the  air, 
and  M.X  the  weight  of  the  vapor  at  any 
instant. 

The  dilatation  or  compression  of  the 
mixture  of  the  vapor  and  air  is  effected 
in  such  manner  as  to  satisfy  the  differ- 
ential equation  : 

mcdt  +  M(rfy  +  dxp)  =  -  APcZ  V.  (69) 
which  expresses  the  fact  that  variations 
in  the  internal  heat  of  the  mixture  equal 
the  variations  of  work  accomplished. 

We  have  also 

dq^zcfa 
c  being  the  specific  heat  of  water. 

The  differential  equation  can  then  be 
written 

t=  —  M.dxp 


p  being  the  tension  of  the  vapor,  and  P 
that  of  the  mixture. 


59 

But  xp=xr- 

dxp=dxr  -  Kpdxu  -  Kxudp. 
and  dN—^lLdxu 

p  is  the  latent  heat  of  the  vapor, 
r  is  the  heat  of  vaporization, 
u  is  the  increase  of  volume  of  a  kilogram 

of  water  vaporized. 
We  know  furthermore  that 


We  have  then 

M.dxp  4-  ApdV  =  M.dxr  --  =^- 
M^  +  AyrfV==Mdyt 

from  which  we  deduce 

.dt  c?V        ^Tjxr 

(me  +  McJrp-  +  Arm  -y-  =—  M^—  . 

Integrating  between  the  limits  Tj  and 


(70) 


60 

V  V 

M.xQ  =  —  and  Mx1  =  —  '> 

—  and  —  are  very  nearly  the  reciprocals 
^^0  it 

of  the  vapor  densities  under  the  pressures 


We  have  furthermore 
T 


Equation  70  will  give  M  when  Tl  and 
T  are  known. 


=  mc(T—  T0) 

-j.)  +  BA-X.P.)  +  A(P,  V-P0Y0) 
or  AWr  =  m^c(T1—  T0) 

+  M.(q—qQ  +  x^—x^)  (71) 

This  equation  gives  the  work  of  resist- 
ance when  M  has  become  known.* 

*  The  two  equations  70  and  71,  which  express  the  re- 
lations between  the  volumes  and  the  temperatures  of  a 
mixture  of  air  and  vapor,  which  is  compressed  or  dilated, 
and  which  determine  also  the  value  of  the  work,  are  ap- 
plicable to  the  Mekarski  motor. 

In  this  machine,  which  is  designed  to  employ  com- 
pressed air,  the  air  is  reheated  just  before  it  is  introduced 
into  the  cylinder  by  being  forced  through  water,  having 
a  temperature  of  100°  to  150°.  The  cylinder  then  con- 
tains air  and  saturated  vapor,  heated  to  a  mean  tempera- 
ture of  100°. 


61 

In  M.  Colladon's  compressors,  into 
which  a  spray  of  water  is  injected,  the 
air  being  compressed  to  four  atmos- 
pheres, the*  temperature  Tx  does  not  rise 
above  50°  centigrade,  the  external  air 
being  about  50°. 

We  deduce  then 

V,    =  0.28429  cu.  metres 

M    =0.57212 

Wr  =  15.291  kilogrammeters. 

When  the  compression  is  effected  with- 
out external  cooling,  we  found  in  §  11 
that  the  work  of  compression  =  17.649 
kilogrammeters,  which  shows  a  gain  in 
the  above  process  of  about  13  per  cent. 

It  remains  to  determine  Wr  for  any 
pressure  without  any  known  value  of  T,. 
'  When  a  certain  volume  of  air  is  dilated 
or  compressed,  with  or  without  the  ad- 
dition of  heat,  the  relation  of  pressure  to 
volume  is  expressed  by  the  equation 
PVa  =  a  constant. 

The  weight  M  of  equations  70  and  71  is  then  the  weight 
of  the  vapor  contained  in  air,  saturated  at  the  tempera- 
ture at  which  it  leaves  the  hot  water. 


62 


(73) 

which  gives 

q-l  log  T.-log  T0 

,  -p,)-log(P.-/).)' 


T1    having  been  found  by   experiment, 
equation  gives  a. 

Making  74  P,  =4  atmospheres,  T1=323° 
and  T0  =  288°  we  find  a  =  1.0912.  a 
being  thus  determined  equation  73  will 
give  Mj.  Only  jflj  being  a  function  of  Tl9 
the  latter  must  be  found  by  successive. 
approximation  s. 
Equation  70  gives 

LroJL^ 

Me  =0.4343  ^°To    u^*  +  0.5888  m. 


r0,  U0  rl  and  w2  are   furnished  by  the 
tables. 

Finally  we  obtain  Wr  by  equation  71. 


63 

The  saturated  air  in  passing  into  the 
cooler  is  reduced  in  temperature  from  T, 
to  T/,  and  a  portion  of  the  vapor  is  con- 
densed. The  weight  of  vapor  remaining 
and  introduced  into  the  expansion  cylin- 
der is : 

V 

"•=57 

— ,  being  the  density  of  the  vapor  cor- 

u\ 

responding  to  the  temperature  T/. 

We  will  calculate  again  the  cooling 
produce  by  the  expansion  and  the  work 
as  explained  in  §  13. 

§  20.  The  following  table  exhibits  the 
results  obtained  from  a  cubic  meter  of 
air  saturated  at  15°,  since  the  sides  of 
the  compressor  cylinder  are  covered  with 
water.  The  weight  of  the  air  is  lfc  021. 


64 


o^ui 


jo 


o  *>• 


O"?  O 

00  ^ 


obtai 


calo 


Negat 


unoq  J9d 


•padopAep 


CQ  t>  CO  CD  O  -H  O> 


.  CO  CO  CO  GQ  O  CO 


CO  CO  O5  CQ  <M  CQ  i-H 


TTi— 

OoOO 


OO 

OO 


5  CO  CO  O  TH  T-H  CQ 

5  CO  1C  1C  CQ  CO  i> 

7-1  SQ  CO  "^  iC  CO 


•90Tra;sis9i  jo 


CO  J>  iO  O  CO  TH  CQ 
CO  00  00  ^  CQ  O5  t*" 

CQ  CO  00  Oi  t>  CQ  CO 

^  CO  O5  -rH  CO  1C  CO 


O5  O5  00  O  CO  ^  O5 
00  O  CO  O  CO^  O 
T-I  i>  CO  O  CO  C3  GO 

•^  Ci  C5  CO  CO 


•paui^qo 


TJ<  t 

CQ 


•;no  SnioS  IITS  jo 


T-i 
CJD       T-I  CO  1O  CO  J 

-§+1  M 


•jossgjdraoo 

UI 


TH  W  03  CO  CO  rJH  -^h 


65 


An  examination  of  this  table  and  a 
comparison  with  the  table  of  §  14  shows : 

1st.  That  the  injection  of  water  into 
the  interior  of  the  compressor  cylinder 
increases  the  efficiency  40  to  50  per  cent. 

2d.  That  the  efficiency  is  at  a  maxi- 
mum at  a  pressure  of  2^  atmospheres. 

3d.  That  it  diminishes,  though  slowly, 
as  we  vary  from  this  pressure. 

4th.  That  the  quantity  of  snow  or  ice 
produced  is  not  greater  than  that  which 
comes  from  the  moisture  of  the  atmos- 
phere. 

The  most  favorable  working  pressure 
apppears  to  be  in  this  case  nearly  4  at- 
mospheres, since  we  obtain  then  a  suffi- 
ciently good  result  (24  to  25  negative 
calories  for  a  cubic  meter  of  air),  with  a 
relatively  good  performance  of  1,200 
negative  calories  per  horse-power  per 
hour. 

Theoretically  the  injection  of  water 
into  the  compressor  affords  a  great  ad- 
vantage. But  it  is  possible  that  the 
water  resulting  from  the  condensation  of 
vapor  in  the  cooler  does  not  all  remain 


66 

in  the  reservoir,  but  that  a  portion  is 
carried  mechanically  into  cylinder  B. 

The  results  indicated  above  for  the 
efficiency  would  in  such  a  case  be  con- 
siderably modified,  and  the  increase  in  the 
quantity  of  frozen  vapor  would  consti- 
tute in  practice  a  grave  inconvenience. 

Experiment  can  alone  decide  this  ques- 
tion. 

We  have  examined  in  the  preceding 
pages  nearly  all  the  problems  belonging 
to  the  air  machine.  We  will  pass  now  to 
the  study  of  the  second  class  of  ma- 
chines, or  those  which  transform  motive 
force  into  negative  heat  by  the  employ- 
ment of  a  liquefiable  gas. 

§  21.  THE  principle  of  these  machines 
is  the  same  as  that  of  the  kind  described 
in  the  last  chapter.  The  gas  is  com- 
pressed, then  deprived  of  its  heat,  and 
finally  caused  to  expand  in  such  a  man- 
ner as  to  lower  its  temperature.  Only 
in  this  instance  the  abstraction  of  the 
heat  which  follows  the  compression,  has 
the  effect  to  liquefy  the  gas,  and  it  is  the 
vaporization  of  the  resulting  liquid  which 


67 

produces  the  lowering  of  the  tempera- 
ture. 

When  a  change  of  volume  of  a  satura- 
ted vapor  is  made  under  constant  press- 
ure, the  temperature  remains  constant. 
The  addition  or  subtraction  of  heat, 
which  produces  the  change  of  volume,  is 
represented  by  an  increase  or  a  diminu- 
tion of  the  quantity  of  liquid  mixed  with 
the  vapor. 

On  the  other  hand  when  vapors,  even 
if  saturated,  are  no  longer  in  contact 
with  their  liquids,  and  receive  an  addi- 
tion of  heat,  either  through  compression 
by  a  mechanical  force,  or  from  some  ex- 
ternal source  of  heat,  they  comport 
themselves  nearly  in  the  same  way  as  per- 
manent gases,  and  become  superheated. 

It  results  from  this  property,  that  refrig- 
erating machines,  using  a  liquefiable  gas 
will  afford  results  differing  according  to  the 
method  of  working,  and  depending  upon 
the  state  of  the  gas,  whether  it  remains 
constantly  saturated,  or  is  superheated 
during  a  part  of  the  cycle  of  working. 
/  §  22.  We  will  suppose  first  that  the 


68 

gas  is  constantly  saturated  and  will 
examine  the  conditions  to  be  fulfilled 
under  this  hypothesis,  and  the  results 
that  may  be  obtained. 

Employing  the  notation  of  the  preced- 
ing chapter  we  will  designate  by  m  the 
weight  of  the  gas  employed,  P2  and  T2, 
the  pressure  and  the  absolute  tempera- 
ture of  the  cooled  gas,  P,  and  T/,  the 
pressure  and  the  absolute  temperature 
in  the  condenser. 

The  pressures  P2  and  Pa  are  deter- 
mined by  the  temperatures  T2  and  T/; 
These  are  the  pressures  of  a  saturated 
vapor  at  these  temperatures,  and  are 
given  in  Kegnault's  tables. 

The  temperature  of  the  condenser  is 
determined  beforehand  by  local  condi- 
tions. Depending  on  the  surface,  the 
interior  of  the  condenser  will  exceed  by 
5°  or  10°  the  temperature  of  the  water 
furnished  to  the  exterior.  This  latter 
will  vary  from  11°  or  12°  C  the  tempera- 
ture of  water  from  considerable  depth 
below  the  surface,  to  30°  or  35°,  the 
temperature  of  surface  water  in  hot 


69 

climates.  The  volatile  liquid  employed 
in  the  machine  ought  not  at  this  temper- 
ature to  have  a  tension  above  that  which 
can  be  readily  managed  by  the  appa- 
ratus. 

On  the  other  hand  if  the  tension  of 
the  gas  at  the  minimum  temperature  is 
too  low,  it  becomes  necessary  to  give  to 
the  compression  cylinder  large  dimen- 
sions, in  order  that  the  weight  of  vapor 
afforded  by  a  single  stroke  of  the  piston 
shall  be  sufficient  to  produce  a  notably 
useful  effect. 

These  two  conditions,  to  which  may 
be  added  others;  such  as  those  depend- 
ing on  the  greater  or  less  facility  of 
obtaining  the  liquid,  upon  the  dangers 
incurred  in  its  use  either  from  its  inflam- 
mability or  unhealthfulness,  and  finally 
upon  its  action  upon  the  metals,  limit 
the  choice  to  a  small  number  of  sub- 
stances. 

The  gases  or  vapors  in  use,  are; 
Sulphuric  Ether,  Sulphurous  Oxide,  Am- 
monia and  Methylic  Ether. 

The    fo0jrki'   ^ed    from 


((UNIVERSITY] 

Vv.  ^f  f~\  -CP  / 


70 


Regnault  exhibits  the  tensions  of  the 
vapors  of  these  four  substances  at  differ- 
ent temperatures  between— 30°  and  +  40°. 
The  original  tables  expressed  the  ten- 
sions in  millimeters  of  mercury.  To 
facilitate  computation,  the  tensions  are 
here  given  in  kilograms  per  square 
meter. 


Tempera- 
ture. 

Sulpuric 
Ether. 

Sulphur 
Dioxide. 

Ammonia. 

Methylic 
Ether. 

—40 

7.187 

—35 

— 

— 

9.302 

— 

—30 

— 

3.908 

11.918 

7.837 

—25 

— 

5.082 

15.120 

9.736 

—20 

917 

6.519 

19.003 

11.992 

—15 

1.194 

8.265 

23.669 

14.652 

—10 

1.541 

10.366 

29.225 

17.765 

—  5 

1.968 

12.  $74 

35.797 

21.380 

0 

2.493 

15.840 

43.475 

25.547 

+  5 

3.129 

19.322 

52.405 

30.318 

+10 

3.894 

23.378 

62.707 

35.743 

+15 

4.808 

28.074 

74.504 

41.873 

+20 

5.891 

33.474 

87.925 

48.755 

+25 

7.164 

39.645 

103.073 

56.437 

+30 

8.651 

46.659 

120.083 

64.961 

+35 

10.377 

54.585 

129.054 

— 

+40 

12.367 

63.496 

160.112 

— 

An  inspection  of  the  table  shows  at 
once  that    the  use  of  ether  does  not 


71 

readily  lead  to  the  production  of  low 
temperatures  because  its  pressure  be- 
comes then  very  feeble. 

The  ether  machine  is,  however,  aban- 
doned. Ammonia  on  the  contrary  is  well 
adapted  to  the  production  of  low  temper- 
atures ;  but  its  elastic  force  is  very  great 
at  temperatures  from  15°  to  30°  which 
are  readily  produced  in  the  condenser. 
It  is  not  a  good  aid  to  the  transformation 
of  mechanical  force  into  heat,  on  account  of 
the  difficulty  of  maintaining  tight  joints 
in  the  apparatus,  and  of  the  influence  of 
waste  spaces  at  the  high  pressures. 
Methylic  ether  yields  low  temperatures 
without  attaining  too  great  pressures  at 
the  temperature  of  the  condenser. 
Finally,  sulphur  dioxide  readily  affords 
temperatures  of— 10°  to  — 15°  while  its 
pressure  is  only  3  to  4  atmospheres  at 
the  ordinary  temperature  of  the  con- 
denser. These  two  latter  substances 
then  lend  themselves  conveniently  for 
the  production  of  cold  by  means  of 

x  mechanical  force. 


72 

§  23.  Let  c  be  the  specific  heat  of  the 

liquid  employed. 
q  the  quantity  of  heat  neces- 
sary to  raise  1  kilogram 
of  the  liquid  from  0°  to 
T°-273°. 


/\,  r,  p,  the  total  heat,  the  heat  of  vapor- 
ization, and  the  latent  heat  of  the 
vapor  considered  at  the  temperature 
T°-273. 

«,  the  increase  of  volume  of  one  kilo- 
gram of  liquid  vaporizing  at  T°—  273°. 

We  have  by  definition 


We  will  apply  indices  to  these  quanti- 
ties similar  to  those  which  affect  the  let- 
ter T  in  designating  the  different  abso- 
lute temperatures. 

In  order  that  the  vapor  be  constantly 
saturated,  it  is  necessary  that  the  quanti- 
ties of  liquid  and  of  vapor  taken  into  the 
compressor  at  once  be  such  that  at  the 
end  of  the  compression  all  the  liquid 


73 

shall  be  vaporized  and  the  vapor  shall 
not  be  superheated. 

If  we  let  x'  '2,  represent  the  proportion 
of  vapor  contained  in  the  mixture  at  the 
commencement  of  the  inflow,  the  work 
of  compression  will  be  equal  to  the  dif- 
ference in  the  amount  of  internal  heat  of 
the  mixture  at  the  beginning  and  end  of 
the  compression,  that  is  to  say  to 

™(?/-?2  +  P/-<P,)- 

The  work  of  the  inflow  into  the  con- 
denser will  be  Pt  V1?  calling  V/  the  vol- 
ume occupied  by  a  weight  m  of  the 
vapor  at  the  end  of  the  compression, 
and  the  work  of  the  back  pressure  will 
be  P2  Va,  V2  being  the  volume  occupied 
by  the  weight  mx^  of  vapor. 

We  have  also 


and  V,=»<«,  +  -,        (75) 

6  being  the  density  of  the  liquid  sup- 
posed constant. 

We  may  neglect  the  fraction  which  is 
very  small,  and  write 


74 


from  which  we  may  get 


and  m  rz  —  mp^  +  AP2  Va. 

The   total   work   of    the   compression 
'  including  the  outflow  is 

AW,  =».(?',-?,  +  »•',-*>,).     (76) 
As  the  compression   follows  an  adia- 
batic  curve,  the  quantities  qf  ^  q^  r\,  ra, 
T',  and  T2  bear  the  following  relation: 

T'i 

/cc&      tc;2r^       rrt 
Ts  T~=="fr~T'1 

or  more  simply, 


TjfT  —  "rfi     • 
*"!  *-i 

Equation  (77)  will  give  the  quantity 
<#'„.  Consequently  equation  (75)  fur- 
nishes, when  we  know  m,  the  volume  V2 
that  the  piston  should  describe  during 
the  aspiration  in  order  that  all  the  liquid 
should  be  vaporized  at  the  end  of  the 
compression;  or,  inversely,  the  weight  m 
may  be  found  if  V2  be  given. 


75 

The  vapor  flows  into  the  condenser 
where  it  is  liquefied. 

The  heat  absorbed  by  the  water  of  the 
condenser  is 

Q1=»ir'1  (78) 

The  liquid,  then  passes  into  the  ex- 
pansion cylinder  where  it  is  vaporized, 
producing  work  till  it  attains  the  press- 
ure P2  and  the  temperature  T2  of  the 
refrigerant.  At  the  end  of  the  expan- 
sion, the  weight  of  vapor  in  the  mixture 
is  mx^. 

The  work,  including  the  counter- 
pressure,  and  neglecting  the  work  of 

introducing  the  liquid,  pl—     '  '™,  which 
is  very  small,  is  ; 

AWm=wi(^1-Sri-aj9ri).          (79) 

and  the  equation  of  the  adiabatic  curve 

is 


which  determines  x'9. 

The  quantity  of  heat  Q  necessary  to 
bring    the    mixture     whose     weight    is 


76 

m(l—  #2)  of  liquid  and  m#2  of  vapor  to 
its  primitive  condition,  in  which  m(l-#'2) 
is  the  weight  of  the  liquid  and  mx\  is 
the  weight  of  the  vapor,  is, 

Q=wi(a5's-a;2)ra 
or  by  reason  of  equations  (76)  and  (79) 

Q=  ^  mr\  (81) 

The  work  expended  is  Wr  —  Ww  and  we 
have 


(82) 

The    theoretic    performance    of    the 
machine  is 


a  result  already  found  in  section  3,  and 
which  is  identical  with  that  at  which  we 
arrived  in  the  case  of  permanent  or  non- 
liquefiable  gases. 

§  24.  We  will  now  take  a  numerical 
example,  and  consider  the  dimensions  of 
the  cylinders  to  be  so  regulated  that  a 
final  temperature  of—  15°  is  obtained,  the 
temperature  of  the  condenser  being 


77 


°,  and  the  volume  of  gas  taken  into 
the  compressor  at  each  stroke,  V2=one 
cubic  meter. 

The  resolution  of  the  above  equa- 
tions supposes  a  knowledge  of  the 
values  of  r,  q,  c  and  u,  or  APw.  They 
have  been  determined  directly  by  Reg- 
nault  for  sulphuric  ether,  but  not  for 
sulphur  dioxide,  ammonia  and  methylic 
ether.  Availing  ourselves  of  the  experi- 
ments of  Regnault  upon  the  compressi- 
bility of  gases,  we  have  been  able  to 
determine  these  quantities  for  sulphur 
dioxide  and  ammonia  and  prepare  tables 
giving  results  for  every  five  degrees  from 
-30°  to  +  40°. 

The  method  of  calculation  of  these 
tables  will  be  found  in  a  note  at  the  end 
of  this  essay. 

For  sulphur  dioxide  we  find, 


«'1=+18orTa=291 
,=    95.015  r=    87.23 


2=  -5.4615 
=    0.419 


78       • 

The  table  of  §  22  gives  P2=8265  and 
^=31170. 

Making  the  calculations  indicated  by 
the  equations  (77)  and  (80)  we  find 
^=93.29  per  cent. 
xz  =11.90  per  cent. 
Equation  (75)  gives 

m=2.554  kilograms. 

Equations  (76)  and  (79)  give 

AWr=27.08  whence  Wr=11.482  k'g'm. 

AWm=  1.82  whence  Wm=     772  k'g'm. 

Finally  equations  (78)  and  (81)  give 


Q  =197.56 

Thus  the  volume  described  by  the 
piston  of  the  compression  cylinder  being 
one  cubic  meter,  2*,  5  54  of  sulphur  diox- 
ide working  between  —15°  and  -f  18° 
produce  197.50  negative  calories.  To 
effect  this  it  is  necessary  to  introduce 
into  the  compressor  cylinder  at  each 
stroke  a  mixture  of  liquid  and  gas  of 
which  the  proportion  should  be  93.29 
per  cent,  of  gas  and  6.71  per  cent,  of 
liquid. 


79 
,  We  have  for  ammonia 


Pz=   23669  P'1=  82183 

r,=    322.53  r\  =  301.70 

w,=    28.604  APX!=  31.431 

u^=     0.512  <  =  0.1621 

&=-  14.68  q\  =  18.696 

The  mean  specific  heat  of  the  liquid  at 
0°,  c=1.0058. 

By  means  of  these  given  values  we 
find 

3^  =  92.62  per  cent. 

x\=  9.68  per  cent. 

m=  2*  .1034 

AWr  =  76.55  Wr  =  32,457  k'g'm 

AWm=     4.52  Wm=  1,917  k'gm 

Q:  =634.59 

Q  =562.56 

2^.1034  of  ammonia  working  between 
the  same  limits  of  +18°  and  —1°  and 
with  the  same  dimensions  of  compressor 
cylinder  as  before  furnish  562.56  nega- 
tive calories  per  hour. 

.  We    will   now   consider   ether.      The 
vapor  of  ether,  unlike  steam,  superheats 


80 

during  expansion  and  condenses  during 
compression.  An  ether  machine  ought, 
therefore,  to  work  so  that  only  vapor  is 
introduced  into  the  compressor  cylinder, 
and  not  a  mixture  of  liquid  and  vapor. 
At  the  end  of  the  compression  a  part  of 
the  vapor  becomes  condensed. 

We   shall   then   have  #'2=1   and  the 
equations  above  found  become: 
0,001\ 


0,001 


Q  =m(l— 


The  empirical  formulas  established  by 
Eegnault  for  the  vapor  of  ether  are  : 
r=94,00—  0,0790*—  0,0008514#2, 


^=0,52901^  +  0,0002959^. 


81 


and  we  deduce  : 

for         £=—15          and 

P2=1194  kilog. 

r,=  94963, 
APA  =  7,014, 

^=2,491, 

2,=  -7.868, 


t=+l$, 
P1=5456, 
^=92,302, 
^,  =  7,516, 


^=9,618, 
c=0,5299, 
and  we  have         tf=  0,736. 

Performing  the  calculations  indicated, 
we  find, 

^,=17.85, 


Q=31e.38, 
r  =4.44, 
AWTO=0.42, 

The  same  machine  working   between 
—15°   and    +18°,   will    give   per   cubic 
meter  of  — 
Ammonia  ......  562.56  negative  calories. 

Sulphur  dioxide.  197.56 
Sulphuric  ether.    31.38 


" 


82 

The  efficiency  would  be  0°,0184  per 
kilogrammeter. 

§  25.  We  remark  here  that  the  positive 
work  Wm  is  always  small  compared  with 
the  negative  work  W,-. 

We  can  then  without  great  loss  of 
power  simplify  the  machine  by  suppress- 
ing the  expansion  cylinder  and  replacing 
it  by  a  simple  cock  so  regulated  as  to  de- 
liver into  the  cooler  a  quantity  of  liquid 
precisely  equal  to  the  amount  admitted 
to  the  compressor  to  obtain  the  determ- 
ined cooling  effect. 

The  cycle  of  operations  is  not  revers- 
ible.    We  shall  have  — ^-^--SL,  but 
AWr     Q,-Q' 

the  proportion  will  be  less  than 

%— y 
T 

rp,  _J,~  ,  and  the  efficiency  would  be  less. 

•*•    1          ^2 

This  manner  of  working  is  represented 
in  the  diagram,  Fig.  1,  by  replacing  the 
adiabatic  line  V^V,  by  the  two  right 
lines  V^V",  and  V'"2V"2  situated  to  the 
right  of  the  point  V2.  The  quantity  Q 
proportioned  to  V"2V0  is  less  than  the 


83 


84 

quantity  Q  of  the  preceding  case  which 
was  proportioned  to  V2'V0,  and  the  quan- 
tity Qj  —  Q  will  be  augmented  by  a  quan- 
tity proportional  to  the  area  V^V'^V,. 

The  equations  (76),  (77)  and  (78)  re- 
main unchanged. 

The  weight  m  of  the  liquid  under  the 
pressure  P1  and  the  temperature  T\ 
passing  suddenly  into  the  refrigerator, 
a  part  of  the  liquid  is  vaporized;  the 
temperature  of  the  mixture  becomes  T2 
and  the  pressure  P2.  The  quantity  cc2  of 
liquid,  which  is  vaporized,  is  given  by 
the  equation 


0.001.ra_  n 
~^~ 

which  shows  that  the  variation  of  inter- 
nal heat  mtyz—q'^+XtPs)  is  equal  to  the 
exterior  work  accomplished  ; 


V'2  being  the  volume  occupied  by  the 
weight  mx^  of  vapor  after  the  passage  of 
the  mixture  into  the  refrigerant. 


85 


We  have  V'2=ra 

If  we  neglect  the  very  small  quantity 

0.001  ra 
Li-~  6~ 
the  preceding  equation  becomes*: 

ay^'i-ft  (84) 

The  quantity  Q  is  again  given  by  the 
equation 


or  by  reason  of  eq.  (76) 

•Qzzmr^-AWr  =  C^- 
from  whence  the  performance 


The  efficiency  will  be  less.  It  is  easy 
to  show  that  the  value  of  x^  given  by 
eq.  (84)  is  always  greater  than  that  given 
by  eq.  (80).  Consequently  the  value  of 
Q  will  be  less  in  the  second  case  than  in 

the  first,  and  the  ratio—  —  ^-  will  also  be 

v^—  y 

less. 

In  applying  equations  (84)  and  (85)  to 
the  same  cases  as  those  of  §  24,  we  find 
for  sulphur  dioxide 


86 

cc2  =  12.64  per  cent. 
Q=195.71 

and  the  performance=0.c0170  per  kilo- 
grammeter.     For  ammonia : 

a;2  =  10.35  per  cent. 
Q=558.11 

and  the  efficiency  0.C0172. 
Finally  for  sulphuric  ether 
#2= 18.46  per  cent. 
Q=:30.96 
efficiency = Of  0164 

§  26.  In  order  to  realize,  either  the 
cycle  of  Carnot  or  the  non-reversible  cycle 
indicated  above,  it  is  necessary,  when  we 
employ  a  liquefiable  gas  which  superheats 
under  compression,  to  introduce  into  the 
compressor  cylinder  at  each  aspiration,  a 
mixture  of  liquid  and  vapor  in  such  pro- 
portions that  it  shall  all  be  in  the  state  of 
gas  at  the  end  of  the  compression. 

We  can  devise  no  practical  means  of 
realizing  this  condition.  So  we  content 
ourselves  when  employing  freezing  ma- 
chines that  use  a  liquefiable  gas,  with 


87 

introducing-  into  the  compressor  the  gas 
without  any  mixture  of  liquid.  It  hap- 
pens then  with  sulphur  dioxide  and  am- 
monia that  the  gas  superheats  during  com- 
pression,, and  therefore  that  during  a  part 
of  the  operation  the  machine  acts  like  the 
air  machine. 

It  is  clear  that  under  these  conditions 
we  augment  the  range  of  temperature 
between  T,  of  the  gas  arriving  in  the  con- 
denser, and  T2  of  the  refrigerant,  and 
consequently  of  the  useful  effect  of  the 
apparatus. 

Referring  again  to  Fig.  1  we  see  that 
we  start  with  a  volume  VQ  greater  than  V0 
of  the  preceding  casey  compress  the  vapor 
to  the  volume  vl  following  the  adiabatic 
curve  v0v,  of  the  superheated  gas;  cool 
it  from  the  temperature  Tt  to  the  temper- 
ature T/  corresponding  to  its  liquefaction 
under  the  pressure  Pr  It  is  then  passed 
into  the  refrigerant  either  producing  work 
and  describing  the  adiabatic  curve  VjV2 
or  by  means  of  a  cock  by  which  means  it 
describes  the  lines  V/V,'"  and  V/"V./'. 

The  quantity  of  negative  heat  gained 


88 

by  superheating  is  represented  by  the 
length  V0v0  and  the  increase  of  resistant 
work  by  the  area  V^v^. 

Tracing  from  the  point  VQ  the  adiabatic 
curve  of  the  saturated  vapor,  the  point 
v/  will  be  to  the  left  of  v^ 

If  the  compressed  vapor  follows  the 

Q' 

adiabatic  VQV^  the  performance  ^— — -= 

^!     —  <J 

Q 

will  be  equal  to  the  performance  -~ ^ 

of  the  cycle  V.V.V/V,. 

But  as  the  compression  follows  the 
line  vQvl  we  see  that  for  the  same  quan- 
tity Q'  of  obtainable  negative  heat,  the 
quantity  Q1  —  Q  would  be  greater  than  a 
quantity  proportional  to  the  area  VQVV\. 

We  can  say,  then,  that  a  priori,  the 
theoretic  efficiency  of  freezing  machines 
working  so  as  to  superheat  the  gas  is 
less  than  that  of  machines  that  work 
without  superheating. 

The  difference  is  small  as  we  shall  see 
later. 

?  27.  We  will  now  examine  the  condi 
tions  of  working  of  a  machine,  under  the 


89 

supposition  that  we  introduce  into  the 
cylinder  during  aspiration  only  gas,  and 
in  such  condition  as  to  superheat  during 
compression. 

A  certain  volume  V2  of  gas  under 
pressure  P2  and  temperature  T2,  it  is  re- 
quired to  find  its  volume  V,  and  its  tem- 
perature Tj  when  it  shall  have  attained 
the  pressure  P}  of  the  condenser. 

If  liquefiable  gases  behaved  as  do  per- 
manent gases,  it  would  suffice  to  use  the 
equations  (1)  to  (6),  which  were  estab- 
lished in  §  10  for  the  compression  of  air. 

But  the  researches  of  Regnault  on  the 
compressibility  of  gases,  have  established 
the  fact  that  when  near  the  liquefying 
point  these  bodies  are  far  from  following 
the  laws  of  Mariotte  and  Gay  Lussac 
upon  which  the  formulas  which  we  have 
used  were  founded. 

Zeuner  has  given  (Theorie  Mecanique 
de  la  Chaleur)  the  result  of  hi^  researches 
upon  superheated  steam. 

He  found  the  following  relation  to  ex- 
ist between  the  pressure  P,  the  volume 
of  the  unit  of  weight  (specific  volume) 
v,  and  the  absolute  temperature  T, 


90 

Pv=BT-CPn  (86) 

in  which  C  and  n  are  constants  to  be  de- 
termined by  experiment 

B=%!*  (87) 

A. 

Cp  being  the  specific  heat  of  the  vapor 
under  constant  pressure,  which  is  con- 
stant according  to  Regnault. 

If  we  make  &=f,  B=50.933  and 
0=192.50,  we  find  that  this  formula  fur- 
nishes for  the  specific  volume  of  steam, 
numbers  which  agree  remarkably  well 
with  the  results  of  experiment. 

Zeuner  does  not  offer  this  relation  as 
rigorously  exact,  but  as  giving  much 
better  results  than  the  formula, 

P^=RT  which  applies  to  permanent 
gases. 

Liquefiable  gases  being  nothing  but 
superheated  vapors,  we  will  employ  equa- 
tion (84)  established  for  superheated 
steam,  but  will  determine  the  constants 
in  each  case  employing  the  results  of 
Regnault's  experiments  upon  the  dilata- 
tion and  compression  of  gases. 


91 

If  we  call  a  the  coefficient  of  dilatation 
of  the  gas  under  atmospheric  pressure, 
it  is  easy  to  see  that  eq.  (86)  gives : 

1 
«=  —    ~7sr~ 

273 --^-.10.334" 
13 

and  10.334?;0=:273B-C.  10334",  (88) 
whence  10.334v0a=B.  (89) 

an  equation  which  gives  B  when  we  know 
the  coefficient  of  dilatation  and  specific 
volume  v0  at  0°  and  atmospheric  pressure. 

If  the  relation  (87)  were  exact,  it  would 
suffice  with  equations  (88)  and  (89)  for 
determining  B,  C  and  n.  But  the  num- 
bers thus  obtained  do  not  coincide,  at  least 
in  the  case  of  sulphur  dioxide  and  am- 
monia with  the  results  obtained  by  Beg- 
nault.  Instead  therefore  of  using  equa- 
tion (87)  we  will  determine  n  by  one  of 
the  results  found  by  Begnault  for  the 
product  PY. 

Begnault  gives  values  of  PV  for  tem- 
peratures of  1.7°  for  sulphur  dioxide,  for 
8.1°  for  ammonia  and  for  pressures  vary- 
ing from  600  to  1200  and  1400  millimeters 


92 

of  mercury.  We  can  deduce  from  these 
tables  the  volume  V0  at  0°  and  under  press- 
ure of  760  millimeters,  and  then  calculate 
the  weight  m  of  the  gas  required  in  our 
examples.  We  then  have 

PV^^BT-mCP71  (90) 

which  combined  with  equation  (89)  will 
furnish  C  and  n. 
For  sulphur  dioxide 

«=0.0039028;  v0=0.3442 
For    P=16.345ksm-   and    T  =  274.7. 
Kegnault  found, 

py 

— =3526.16 
m 

We  deduce  B^13.882 
C=3.8455 
n= 0.44487 

Introducing  these  constants  into  equa- 
tion (86)  we  can  obtain  for  Pv  values 
which  coincide  in  a  satisfactory  manner 
with  Regnault's  results. 

These  values  are  slightly  less  than  Keg- 
nault's  for  pressures  between  10.334  kg. 
and  16.345  kg.,  and  a  little  larger  for 


93 


pressures  lying  beyond  these  limits  on 
either  side. 

For  ammonia  we  unfortunately  do  not 
know  the  coefficient  of  dilatation ;  it  was 
not  determined  by  Regnault.  As  this 
gas  is  near  its  liquefying  point  at  0°  we 
will  assume  its  coefficient  to  be  about  the 
same  as  that  of  sulphur  dioxide  and  cyano- 
gen, which  is  0.0039.  In  the  absence  of 
exact  values  determined  by  experiment  it 
is  clear  that  results  obtained  under  the 
above  assumption  can  be  regarded  as 
approximative  only. 

We  have  v0=l. 2977  and  Eegnault's 
tables  give : 

PV 
-=13596  for  T=281.1°  and  P=19515 

7)1  kgm. 

We  then  deduce 
B=52.4943,      0=43.7144,     rc=0.32685, 

§  28.  It  remains  now  to  find  the  equation 
of  the  adiabatic  curve  of  a  superheated 
vapor,  of  which  the  pressure,  the  specific 
volume  and  the  temperature  are  related 
as  follows : 


94 

The  fundamental  equation  of  the  me- 
chanical theory  of  heat  is,  calling  Q  the 
quantity  of  heat  furnished  to  a  body,  U 
its  internal  work,  and  supposing  the  ex- 
ternal pressure  is  always  equal  to  the 
expansive  force  : 


and  as  TJ  is  a  function  of  p  and  v,  we 
have: 


Assuming    -=-  =J     -^-, 
dp  dv 

-we  have        cZQ=A  (Kdp  +  Ydv)         (91) 

or  rfQ=A 

;and  since  dU  is  an  exact  differential, 


__ 

dv  ~~  dp 

We  know  that  the  factor  ^is  the  fac 

tor  of  integrability  of  the  function  ILdp 
.;  and  we  deduce 


95 

*         m_y^   V*  /Q0\ 

*4?       tfV 

We   also   have   in  virtue  of   equation 
(86),, 

dt     v 


cTp:B<  ~TT~ 

dt      p 
and  _=J_. 

dv     B 

If  we  suppose  that  the  pressure  remain 
constant,  dp  =  Q,  and  eq.  (91)  gives 


But,  dQ,p=cpdt,  calling  cp  the  specific 
heat  at  constant  pressure,  which  we  sup- 
pose constant  and  which  is  known.  We 
have  then  : 

_Cpdt^_Cp_^ 

~A  dv~~A 
and  from  eq.  (92), 

T>np 


and  finally, 
ofQ=A 

do  +  vdp)-vdp  + 


(93) 


96 


For  the  equation  of  an  adiabatic  curve, 
it  is  necessary  to  make  dQ—  0.  We  have 
then  : 


(94) 

Introducing  the  value  of  T  from  equa- 
tion (86),  it  becomes. 

cv      dt    dp  ,.         cp  7m     . 

AB~~T=p  integrating   |g£F=3p 

-f  const. 
or  finally 

(W 

an  equation  analogous  to  equation   (4) 
which  we  found  for  air. 

Replacing  T  by  this  value  in  equation 
(86)  we  get  finally  for  the  equation  of  the 

adiabatic  curve 

AB 


(96) 

mits, 
for  superheated  steam,  this  equatioji  be- 


If  —  be  equal  to  n,  as  Zeuner  admits, 


97 

comes  pvk=&  constant,  and  it  is  similar 
to  that  which  represents  the  adiabatic 
curve  of  the  permanent  gases. 

Eq.    (94)  gives  the  work  of  compres- 
sion 

pdo=  - 

whence 


n-p»]  (97) 
or  again 


and 


(99) 

§  29.  We  can  now  establish  the  equa- 
tions relating  to  the  compression  of  a 
liquefiable  gas  in  a  cylinder.  A  weight 
m  of  gas  occupying  the  volume  V2  at  the 
temperature  T2,  and  under  the  pressure 
P2  is  compressed  until  the  pressure  is  P, 
of  the  condenser.  The  temperature  Ti 


98 

at  the   end  of   the  compression  will   be 
given  by  the  equation  (95). 

AB 

(100) 


and  the  work  of  compression  including 
the  flowing  of  the  the  gas  is 


C(P»-P») 


m  is  given  by  the  equation 

P  V  V 

•*•  Y  Y2 


""BT~-OPS""          0.001 
^  +  -d~ 
the  final  volume 

P  BT  —  CPn 
V  —V     2        *     V^-LJ. 

1-    2P;BT2-CPJ 

We  cool  the  gas  in  the  condenser  under 
constant  pressure.  The  volume  Y1 
becomes  V/  at  the  moment  the  temper- 
ature becomes  T/;  since  the  gas  is  lique- 
fied we  have; 


99 

P  BT  '  —  CPn 

V  '  —  V—  2  —  ^—        i 

2P;BT2-CP£ 

and  the  quantity  of  heat  removed  from 
the  condenser  is  : 

Q^mcp  (T^T/J  +  mr/         (103) 
The  volume  occupied  by  the  liquid  is 

O.OOl.ra 

*,=  -*- 

tf  being  the  density  of  the  liquid  supposed 
constant. 

The  liquid  is  then  passed  into  the  re- 
frigerant without  producing  work. 

The  quantity  mx^  of  gas  which  vapor- 
izes while  the  pressure  passes  from  Px  to 
P2  and  the  temperature  from  T/  to  T2  is 
by  equation  (84); 

mx^=m(q^-q^. 

The  quantity  of  negative  heat  obtained 
is: 

Q=m(l-aja)ra 

or  Q=^(At-?1')  (104) 

and  we  have 


or 


100 

We  can  verify  the  equality  Qt  —  Q=  AWr 
or 


Keferring   to   the   fundamental    equa- 
tion 


and  making  dQ=O  it  becomes 

mc£  U  —  —  mPdv  =  — 
and  consequently 


(P»-P»)    (105) 
We  have  furthermore  by  definition, 


an  equation  which  signifies  that  the  total 
heat  of  the  vapor  at  t°  is  equal  to  the  in- 
ternal heat  ATI  augmented  by  the  ther- 
mal equivalent  of  the  work  of  vaporiza- 
tion and  dilatation. 
We  have  then 

A,-A,=CP  (^-TJ-^P^-P") 

Hi 

This  equation  is  applicable  to  a  super- 
heated vapor  above  its  point  of  satura- 
tion. 


191 

It  applies  also  at  the  point  of  satura- 
tion ;  we  have  then 


which  verifies  the  equation 
Q^Q^AW,. 
Equation  (105)  can  be  written  : 


C(P"-P») 

=0. 
the  equation  becomes 


C        1 

If  we  make  -~-  --  =0. 
AB      n 


Under  this  form  it  expresses  Him's 
law  of  superheated  vapors,  and  may  be 
thus  expressed:  —  from  the  point  of  con 
densation,  to  the  point  at  which  the  super- 
heated vapor  possesses  the  same  proper- 
ties as  the  permanent  gases,  the  product 
pv  remains  constant  while  the  internal 
work  remains  the  same. 

But  the  equation 


102 


is  not  verified  for  the  cases  of  the  two 
liquefiable  gases  which  we  have  studied, 
and  consequently  we  cannot  apply  to  them 
the  law  of  Him. 

§  30.  We  will  now  take  a  numerical 
example  and  suppose  as  in  the  preceding 
case,  that  a  cubic  meter  of  gas  is  admitted 
at  the  temperature  of  —15°  under  a 
pressure  corresponding  to  this  temper- 
ature, and  that  it  is  compressed  until  its 
tension  is  that  of  the  condenser  and  that 
the  temperature  of  this  latter  is,  in  the 
interior,  +18°. 

Sulphur  dioxide.   Equation  (102)  gives 


Equation  (100)  gives;  making 

cp-  0.15438 
after  Eegnault,  and 

—  =  0.211882; 

Cp 

(p   \  0.211882 
=^     =334.31          or    ^= 


Equations  (103)  and  (104) 


Q=197.75 

whence         AWr  =  Q1  —  Q=28.71 
and  Wr=  121.75 

and  the  theoretic  performance  =0.C0162  or 
4.374  calories  per  horse  power  per  hour. 

In  a  double  acting  engine  working  at 
high  velocity  we  estimate  the  resistances 
at  about  15  per  cent,  of  the  power  ex- 
pended. 

1.15Wr=13.998  and  the  performance 
becomes  0?0141  or  3.807  calories  per 
horse  power,  per  hour. 

This  performance  is  double  that  of  the 
machine  working  with  dry  air  between 
the  same  limits  of  temperature.  This 
difference  shows  not  that  the  air  is  theo- 
retically a  less  efficient  agent  in  the  pro- 
duction of  cold,  but  that  to  produce  the 
same  useful  effect,  the  air  machine  having 
much  larger  dimensions  than  the  liquefi- 
able  gas  machines  will  experience  propor- 
tionally greater  loss  through  resistances. 

§  31.  Generally  with   sulphur  dioxide 


104 

we  do  not  get  as  low  a  temperature  as 
-15°. 

The  opening  of  the  cock  which  leads 
from  the  condenser  to  the  cooler  is  so  reg- 
ulated that  the  pressure  in  the  latter  is 
about  T9¥  of  an  atmosphere,  which  corre- 
sponds to  a  temperature  of  —12°.  41. 
P2=9301kg.  £2=-12°.41. 

With  these  values  the  tables,  given  at 
the  end  of  this  memoir,  give 


r2  =  94.377 
q=  -4.517 
1^=0.3863 

and  by  means  of  equations  (100),  (102), 
(103)  and  (104)  of  §  29  it  is  easy  to  cal- 
culate T1?  Qj,  Q  and  Wr. 

The  results  of  these  calculations  are 
recorded  in  the  following  table,  which 
gives  the  negative  heat  obtained,  the 
work  absorbed  and  the  performance  per 
cubic  meter  of  sulphur  dioxide,  suppos- 
ing the  apparatus  regulated  for  a  tem- 
perature of  —  12°41  in  the  refrigerant,  and 
that  the  temperature  of  the  interior  of 
the  condenser  varies  from  +15°  to  -{-40°: 


105 


op 


calori 


ega 


•jnoq  J8d 
asjoq 


•jnoq  jod 


-,    — .  —     ,    O5  ^ 
.  H  00  CO  tO  CO  TH  00 
I        C3  TJJ  SO  00  CO  O5  O 

°  1O  -^  CO  CO  CQ  0? 


TH  JO  QO  1C  T-I  t- 

.  co  1-1  oj*  co  ao  10 

^  CQ  ,_!  T—  |  -pH  TH  O 

oooooo  o 
oooo  oo 


.toooo?  as  as 


•noiss9iduioo  jo 


TH  CQ  TH 

o" 


A*q 


uosuapuoo 
oqi  jo  aa^AY 


53  CO  CO  CO  CQ 


•T?  'aoissaidraoo 


bnCO  00  rH  CO  O  OO 
O  O  CO  00  Oi  O  TH 
r  rH  rH 


Saipuodssuoo 


.  •  ^i  TJI  10  O  li 
fcpj>  t-  ^H  10  G 

o  o  ^  o  o  t 


jo 


fcj 

-§ 


CQ  C?  CO  CO  ^ 


106 

We  see  that  the  performance  dimin- 
ishes more  than  one-half  when  the  tem- 
perature of  the  interior  of  the  condenser 
rises  from  15°  to  40°. 

The  figures  of  the  last  column  do  not 
nearly  represent  the  number  of  calories 
really  produced  and  utilized.  It  is  nec- 
essary to  take  into  account  the  loss  occa- 
sioned by  the  pipes  ;  the  waste  spaces  in 
the  cylinder ;  of  loss  of  time  in  opening 
of  the  valves ;  of  the  leakage  around  the 
piston  and  valves;  of  the  reheating  by 
the  external  air  ;  and  finally,  when  ice  is 
being  made,  of  the  quantity  of  the  ice 
melted  in  removing  the  blocks  from  their 
molds. 

It  requires  about  100  calories  to  con- 
geal to  —7°  a  kilogram  of  water  taken 
at  15°  or  16°.  Manufacturers  estimate 
that  practically  the  sulphur  dioxide  ap- 
paratus using  water  at  12°  or  13°,  pro- 
duces 25  kilograms  of  ice,  or  2,500  calo- 
ries per  horse  power  per  hour,  measured 
oh  the  driving  shaft,  which  is  about  55 
per  cent,  of  the  theoretic  efficiency  indi- 
cated above. 


107 

*  Fig.  3  represents  the  Pictet  machine 
from  a  design  furnished  us  by  the  invent- 
or. It  has  a  double-acting  compression 
cylinder  with  four  valves.  The  cylinder 
is  furnished  with  a  jacket,  within  which  a 
current  of  cold  water  is  made  to  circu- 
late. 

The  gas  is  compressed  to  a  tension 
corresponding  to  the  temperature  of  the 
water  employed  for  cooling,  generally 
1.8  to  2  kilograms  effective  pressure ; 
then  it  is  discharged  by  the  pipe  T  into 
the  condenser  C  where  it  is  liquefied. 

This  condenser  is  like  the  surface 
condensers  of  marine  engines.  It  has  a 
surface  of  about  24  square  meters  for 
100,000  theoretic  calories  per  hour,  or  48 
square  meters  for  100,000  effective  calor- 
ies per  hour  measured  by  the  ice  pro- 
duced. 

The  quantity  of  water  employed  de- 
pends upon  the  difference  of  temperature 
to  be  allowed  between  the  inside  and 
outside  of  the  condenser. 

If  this  difference  is  to  be  5°  each  litre 
of  water  releases  5  calories  and  the 


108 


109 

quantity  of  water  to  be  employed  will  be 
for  100  theoretic  calories  produced 


, 
"       Q 

which  would  require  for  the  example  of 
§  31  and  for  a  temperature  of  20°  in  the 
condenser,  22.8  litres. 

The  liquid  dioxide  passes  into  the  re- 
frigerant K  by  the  pipe  T',  the  supply 
being  regulated  by  the  cock  r  so  that  the 
pressure  shall  be  T9¥  of  an  atmosphere  in 
the  refrigerant  and  3  atmospheres  in  the 
condenser.  If  the  outlet  by*the  cock  be 
diminished  the  pressure  is  lowered  in  the 
cooler,  and  the  temperature  is  also  low- 
ered, but  the  useful  effect  also  diminishes, 
since  for  the  same  volume  described  by 
the  compressor  piston,  less  weight  of  gas 
is  used.  We  have  in  this  machine,  there- 
fore, the  same  facilities  for  varying  the 
useful  effect  as  in  the  air  machines. 

The  refrigerant  is  constructed  like  the 
condenser.  Its  surface  is  29  square 
meters  for  each  100,000  theoretic  neg- 
ative calories  produced  per  hour.  It  is 


110 

immersed  in  an  incongealable  bath  formed 
of  a  solution  of  calcium  chloride. 

The  temperature  of  the  interior  of  the 
refrigerant  being  —12°,  that  of  the  bath 
being  — 7°.  In  this  bath  are  immersed 
the  tanks  or  moulds  within  which  the 
water  is  frozen. 

Finally  the  sulphur  dioxide  returns  to 
the  compressor  cylinder  by  the  pipe  T". 
The  dioxide  may  be  employed  contin- 
uously so  long  as  no  air  is  permitted  to 
enter  the  joints.  Any  leakage  might  lead 
to  the  production  of  the  trioxide  and  pos- 
sibly sulphuric  acid  which  would  lead  to 
injury  to  machine.  Exceptional  care  is  re- 
quired in  maintaining  tight  joints. 

Some  experiments  with  an  ammonia 
machine  have  not  yielded  very  good  re- 
suls ;  but  the  want  of  success  seems  to 
have  resulted  rather  from  an  imperfect 
action  of  the  surface  of  the  refrigerant  than 
from  any  inherent  defect  in  the  gas  it- 
self. Ammonia  gas  prevents  the  advant- 
age of  affording  about  three  times  the 
useful  effect  as  sulphur  dioxide  for  the 
same  volume  described  by  the  piston. 


Ill 


But  this  advantage  is  balanced  by  the 
inconvenience  of  higher  pressures  and 
consequently  more  leakage,  &c. 

Between  the  limits  of  temperature  of 
12°.41  in  the  refrigerant  and  +  18°  in 
the  condenser  we  find  for  ammonia : 


112 

P2=  26559  kilos. 
r=321.06 


and  we  have  0^=0.50836 


We  deduce  for  each  cubic   meter  de- 
scribed by  the  piston  : 
w=2.163  k. 

T1=342.75         £1=69°.75 
Ql=  709.48 
Q  =627.03 

AWr=Q,-Q=  82.45      Wr=34.959  kg. 
Theoretic  efficiency:    0.0179  or  4.833 
per  horse  power  per  hour. 

"Working  the  apparatus  between  —30° 
and  +18°  we  find. 


2=  330.48 
2=0.9463 
=  -31.82 


^=388.20  ^=115.20 

Qi==370.52 

Q=295.44 


113 


Wr=31.834 

Theoretic  result:  0.00928  or  2505  per 
horse  power  per  hour. 

CHAPTEK  IV. 

MACHINES    EMPLOYING    CHEMICAL    ACTION. 

§  34.  It  remains  to  discuss  the  ice 
making  machines  which  employ  chemical 
affinity  in  their  mode  of  action,  and  of 
which  the  ammonia  machine  of  M.  Carre 
is  the  type. 

Fig.  5  exhibits  the  disposition  of  the 
parts  of  this  apparatus.  It  consists  of  a 
boiler  A  which  contains  a  concentrated 
solution  of  ammonia  in  water;  this 
boiler  is  heated  either  directly  by  a  fire 
as  shown  in  the  figure,  or  indirectly  by 
pipes  leading  from  a  steam  boiler.  The 
condenser  B  communicates  with  the  upper 
part  of  the  boiler  by  the  tube  aa;  it  is 
cooled  externally  by  a  current  of  cold 
water.  The  refrigerant  C  is  so  con- 
structed as  to  utilize  the  cold  produced; 
the  upper  part  of  it  is  in  communication 
with  the  lower  part  of  the  condenser  by 


114 


115 

means  of  the  tube  bb.  The  details  of 
the  construction  are  not  shown  in  the 
figure.  An  absorption  chamber  D  is 
filled  with  a  weak  solution  of  am- 
monia ;  the  tube  cc  puts  this  chamber  in 
communication  with  the  refrigerant  C. 

The  absorption  chamber  communicates 
with  the  boiler  by  two  tubes.  One  ddy 
leads  from  the  bottom  of  the  boiler  to 
the  top  of  the  chamber  D;  the  other, 
ffj  leads  from  the  bottom  of  D  to  the  top 
of  the  boiler.  Upon  the  pipes  ff  is 
mounted  a  little  pump  whose  use  is  to 
force  the  liquid  from  the  absorption 
chamber  where  the  pressure  is  main- 
tained at  about  one  atmosphere,  into  the 
boiler,  where  the  pressure  is  from  8  to 
12  atmospheres. 

The  change  of  temperature  is  managed 
through  the  attachments  to  the  pipes  /'/ 
and  dd  in  a  manner  that  will  be  easily 
comprehended  by  an  inspection  of  the 
figure. 

To  work  the  apparatus  the  ammonia 
solution  in  the  boiler  is  first  heated. 
This  releases  the  gas  from  the  solution 


116 

and  the  pressure  rises.  When  it  reaches 
the  tension  of  the  saturated  gas  at  the 
temperature  of  the  condenser,  there  is  a 
liquefaction  of  the  gas,  and  also  of  a 
small  amount  of  steam.  By  means  of 
the  cock  A,  the  flow  of  the  liquefied  gas 
into  the  refrigerant  C  is  regulated.  It 
is  here  vaporized  by  absorbing  the  heat 
from  the  substance  placed  here  to  be 
cooled.  As  fast  as  it  is  vaporized  it  is 
absorbed  by  the  weak  solution  in  D. 
The  small  quantity  of  watery  vapor  is 
carried  along  mechanically. 

Under  the  influence  of  the  heat  in  the 
boiler  A,  the  solution  is  unequally  satur- 
ated, the  stronger  solution  being  upper- 
most. 

The  weaker  portion  is  conveyed  by 
the  pipe  dd  into  the  chamber  D,  the  flow 
being  regulated  by  the  cock  #,  while  the 
pump  sends  an  equal  quantity  of  strong 
solution  from  D  back  to  the  boiler- 
While  these  exchanges  are  brought 
about  in  the  solutions,  there  is  also  an 
exchange  of  temperatures  whereby  the 
weak  liquid  arrives  cold  in  the  absorp- 


117 

tion  chamber,  and  the  strong  solution  is 
delivered  in  the  boiler  hot. 

The  working  of  the  apparatus  depends 
upon  the  adjustment  and  regulation  of 
the  cocks  g  and  A,  and  of  the  pump;  by 
means  of  these,  the  pressure  is  varied, 
and  consequently  the  temperature  in  the 
refrigerant  C  controlled. 

It  is  seen  that  the  working  is  similar 
to  that  of  the  machines  described  in  the 
preceding  chapters.  The  chamber  D 
fills  the  office  of  aspirator,  and  the  boiler 
A.  plays  the  part  of  compressor. 

The  mechanical  force  producing  ex- 
haustion, is  here  replaced  by  the  affinity 
of  water  for  ammonia  gas;  and  the 
mechanical  force  required  for  com- 
pression is  replaced  by  the  heat  which 
severs  this  affinity  and  sets  the  gas  at 
liberty.  We  see  then  in  advance  that 
we  shall  again  find  a  greater  part  of  the 
equations  already  established  in  the  dis- 
cussion of  the  liquefiable  gas  machines. 

§  35.  We  will  assume  at  first,  that 
under  the  influence  of  the  heat  applied 
to  the  boiler,  ammonia  gas  only  is  driven 


118 

off,  and  no  steam.  We  will  assume  a 
certain  weight  of  the  gas  to  enter  the 
boiler  in  a  state  of  solution ;  being 
heated,  it  will  be  separated  from  the 
water,  requiring  a  certain  quantity  of 
heat  which  we  will  call  Q'.  '  Then,  being 
conducted  to  the  condenser,  it  will  be 
cooled  and  then  liquefied,  and  will  im- 
part to  the  water  surrounding  the  coils  a 
quantity  of  heat  Q,.  In  the  refrigerant 
it  is  evaporated,  borrowing  from  the 
exterior  a  quantity  of  heat  Q ;  it  is  next 
absorbed  by  the  liquid  in  the  chamber  D, 
disengaging  a  certain  amount  of  heat  to 
the  liquid  (which  may  be  deducted  from 
the  total  amount  required  in  the  boiler) ; 
and,  finally,  it  is  reconveyed  to  the 
boiler,  where  it  arrives  in  its  original 
condition.  By  reason  of  the  exchange  of 
temperature  effected  at  E,  all  the  heat  of 
the  weak  solution  going  out  of  the  boiler, 
is  restored  to  the  strong  solution  enter- 
ing it,  so  that  the  changes  of  tempera- 
ture in  the  water  are  effected  without 
expenditure  of  heat. 
In  the  complete  cycle  if  we  neglect  the 


119 

small  amount  of  work  performed  by  the 
pump,  and  the  heating  and  cooling  due 
to  contact  with  the  air,  it  is  clear  that  all 
the  heat  from  external  sources,  being 
Q'  from  the  boiler,  and  Q  from  the 
refrigerant,  will  be  equal  to  the  amount 
Qj  carried  away  by  the  water  of  the 
condenser. 
We  have  then 

Q'=.Qt_Q  and  the 

efficiency  will  be  expressed  by 

which  is  identical 
Qi~  y 

with  that  found  for  the  machines  depend- 
ing on  mechanical  action. 

Q'  the  quantity  of  heat  which  it  is 
necessary  to  expend  in  order  to  produce 
the  quantity  Q  of  negative  calories,  being 
equal  to  Qt  — Q,  has  the  same  value  as 
the  quantity  AWr,  the  calorific  equiva- 
lent of  the  mechanical  work  expended  in 
the  machines  previously  discussed,  to 
produce  this  same  quantity  Q  of  negative 
calories.  We  proceed  to  show  that  be- 
tween the  same  limits  of  temperature  in 


120 


the  condenser  and  refrigerant,  and  for 
the  same  value  of  Q,  the  quantity  Q'  in 
this  class  of  machines,  is  equal,  very 
approximately  at  least,  to  the  quantity 


We  arrive  then  at  this  remarkable 
result  ;  that^in  all  the  ice  machines,  when 
they  work  between  the  same  limits  of 
temperature,  the  theoretic  quantity  of 
negative  heat  produced  is  exactly  the 
same  for  each  calorie  expended,  whether 
it  is  directly  produced  by  chemical  ac- 
tion, or  indirectly  under  the  form  of  me- 
chanical work. 

But  as  a  calorie  represented  by  424 
kilogrammeters  costs  in  the  best  heat 
motors  an  expenditure  of  at  least  10  cal- 
ories in  the  fire,  it  would  seem  that  the 
chemical  machines  possess  a  considerable 
advantage  over  all  the  others,  since  in  these 
latter  the  heat  is  employed  directly,  and 
not  under  the  expensive  form  of  mechan- 
ical work.  Practically,  however,  this  ad- 
vantage is  much  less  than  that  which 
seems  to  result  from  the  above  calcula- 
tions; as  we  will  proceed  to  show. 


121 

§  36.  We  will  assume  the  hypothesis 
mentioned  in  the  beginning  of  the  pre- 
ceding section,  and  determine  the  quan- 
tities Q',  Q1  and  Q  in  terms  of  the  tem- 
peratures, the  pressures  and  weights  of 
the  gas  employed. 

We  will  preserve  the  notations  of  the 
previous  chapter.  Tl  being  the  absolute 
temperature  of  the  gas  as  it  enters  the 
condenser;  T/  its  absolute  temperature 
in  the  condenser,  and  T2  the  absolute 
temperature  in  the  refrigerant. 

Let  m  be  the  weight  of  the  gas  con- 
sidered, occupying  the  volume  V2  at  the 
temperature  T2,  and  under  the  pressure 
P2  at  its  entrance  into  the  absorption 
chamber. 

Let  ATI  be  the  internal  heat  at  the 
temperature  T ;  qe  the  heat  necessary  to 
raise  a  kilogram  of  water  from  0°  to  1°. 

After  the  gas  has  been  absorbed  by 
the  water,  the  absolute  temperature  of 
the  mixture  will  be  T'a. 

During  the  process  of  absorption  of 
the  gas,  there  is  an  amount  of  external 
work  accomplished  equal  to  P2(V2— w),  w 
of  being  the  volume  of  water. 


122 

The  difference  in  internal  heat  before 
and  after  this  operation  is  equal  to  this 
external  work.  We  have  then 


qe  \  +  raATT/-  qe  2  -  mAU2=AP2(V2  -  w). 

The  solution  is  conveyed  to  the  boiler, 
and  there  heated  until  all  the  gas  is 
driven  off.  It  then  occupies  the  volume 
Vj  under  the  pressure  P1?  and  at  the 
temperature  Tr 

The  necessary  quantity  of  heat  Q"  is 
equal  to  the  difference  in  quantities  of 
internal  heat,  augmented  by  the  exterior 
work  accomplished.  This  work  is  equal 
to  PjCVj-w)  less  the  work  of  the  pump, 

(p-p>- 

We  have  then 

Q"=?«  ,-?«  ',  +  wAU.-wAU, 

+  AP,(V-«>)-A(P-P>. 

Adding  this  equation  to  the  preceding, 
member  to  member,  we  find 


This  equation  is  established  without 
taking  account  of  the  effect  of  exchange 
of  temperature.  There  is  furnished  to  the 


123 

solution  which  enters  the  boiler  a  quan- 
tity of  heat  precisely  equal  to  qei-^[e^ 
The  quantity  of  heat  Q'  to  be  supplied 
by  the  boiler,  in  order  to  bring  the 
pressure  of  the  gas  from  Pa  to  PJ?  and 
from  the  temperature  T2  to  Tl  is  then 


-TJ,)  +  AP^-AP.V,     (107) 

The  equations  101  and  105  gave,  in 
case  of  compression  by  a  mechanical 
force, 

AWr=iwA(Ul-Ui)  +  AP.VAP.V, 

which  is  identical  with  the  preceding. 

We  have  then  Q,'=A.~Wr  provided  that 
the  temperature  T,  in  the  case  where  the 
change  of  pressure  of  the  gas  is  obtained 
by  the  heat  combined  with  the  chemical 
action,  is  the  same  as  in  the  case  where 
the  change  is  due  to  a  mechanical  force. 
Experiment  proves  that  it  is  nearly  so. 

It  appears  that  the  temperature  to 
which  it  is  necessary  to  heat  the  am- 
monia solution  to  obtain  a  given  press- 
ure is  higher  as  the  solution  becomes 
weak.  Now  in  the  ice  machines  the  so- 


124 

lution  conveyed  to  the  boiler  contains 
rather  less  of  the  gas  as  the  pressure  in 
the  refrigerant  becomes  more  feeble. 
We  understand  therefore  how  the  tem- 
perature Tx  ought  to  increase  as  the  tem- 
perature Ta  of  the  refrigerant  diminishes. 
Unfortunately,  precise  experiments  upon 
this  point  are  wanting. 

A  series  of  observations  made  by  M. 
Eouart  upon  a  Carre  machine  is  here- 
with given. 

The  first  column  of  each  table  gives 
the  absolute  pressures  in  atmospheres 
and  kilograms ;  the  second  the  tempera- 
tures observed  in  the  boiler ;  the  fourth, 
the  temperatures  of  water  in  the  con- 
denser ;  the  fifth  column  gives  the  tem- 
peratures of  the  liquefied  gas  corre- 
sponding to  the  pressures  in  the  first 
column  (see  table  in  §  22);  the  tempera- 
tures are  those  of  the  interior  of  the 
condenser,  and  are  naturally  more  ele- 
vated than  the  exterior. 

In  the  case  of  mechanical  compression 
the  final  temperature  T,  is  related  to 
the  initial  temperature  and  to  the  initial 


125 

and  final  pressures  as  expressed  by  the 

equation  (100) 

AB 

/PA  cp 


T,=T,  |BV 


The  third  column  of  the  table  gives 
the  temperatures  calculated  by  this  for- 
mula, supposing  T2=243  and  Pa=.ll,918. 

For  the  mean  pressures  the  calculated 
temperatures  coincide  nearly  with  the 
observations.  For  the  higher  pressures 
the  calculated  pressures  are  higher  fchan 
the  observed.  But  it  is  necessary  to 
remark  that  in  this  case  the  watery 
vapor  mixed  with  the  gas  exerts  a  great- 
er influence,  and  that  the  true  gas  press- 
ures ought  to  be  sensibly  less  than  the 
pressures  which  have  served  as  a  basis 
for  calculation. 

The  condensation  in  the  condenser 
and  the  evaporation  in  the  refrigerant, 
are  brought  about  exactly  as  in  the  case 
of  the  machines  acting  by  mechanical 
force.  We  shall  have  then,  as  in  §  27, 


126 


Pressure  in  Boiler. 

Temperature  of  Boiler 

Atm. 

Kilog. 

Observed. 

Calculated 

Degrees. 

Degrees. 

l^j 

15,501 

48 

— 

2 

20,668 

58 

— 

$j£ 

25,835 

65 

— 

3 

31,002 

70 

— 

3J£ 

36,169 

75 

— 

4 

41,336 

80 

— 

4A£ 

46,503 

84 

—  . 

5 

51,670 

88 

— 

5J^ 

56,837 

92 

— 

6 

62,004 

94 

— 

gi^ 

67,171 

100 

— 

714" 

74,921 

106 

106 

7J<2 

77,505 

108 

109 

8 

82,672 

112 

116 

8K 

87,839 

116 

121 

9 

93,006 

120 

127 

9/<2 

98,173 

124 

132 

10 

103,340 

128 

137 

10^ 

108,507 

132 

142 

11 

113,674 

136 

147 

12 

123,998 

142 

156 

13 

134,332 

146 

164 

14 

144,666 

152 

172 

15 

155,000 

156 

180 

15 

155,000 

158 

180 

127 


Temper 
ature  of 
water  of 
con- 
denser. 

Tempera- 
ture 
inside 
of 
condenser 

Differ- 
ence. 

Remarks. 

Degrees. 

Degrees. 

Degrees 

9 





9 

— 

— 

9 





9 

— 

— 

9 

— 

— 

9 

— 

— 

9 





10 
10 
10 

15.0 
16.1 

5.0  \ 

6.1    1 

The  gas  liquefies 
and  the  apparatus 
Begins  to  work. 

12 

18.0 

6.0 

13 

20.0 

7.0 

14 

21.7 

7.7 

15 

23.3 

8.8 

^0 

17 

25.1 

8.1 

JT\ 

17 

26.7 

9.7 

dfa  I 

19 

28.1 

9.1 

/^    * 

24 

31.0 

7.1 

/£*  *- 

30 

32.8 

2.8 

35 

36.0 

1.0 

/  ^/  o  fiT^ 

37 

38.0 

1.0 

/  ^^  to  t^i 

39 

38.0 

— 

[  52S     r* 

oc 


**ff 


**  ^ 


128 


Absolute  pressures. 

Temperature  of  Boiler 

Atm. 

Kilog. 

Observed.  Calculated 

Degrees. 

Degrees. 

3 

31,002 

73 

— 

&A 

46,503 

90 

— 

5 

51,670 

94 

— 

&A 

56,837 

100 

— 

6 

62,004 

103 

— 

V4 

67,171 

106 

— 

7 

72,338 

110 

— 

^A 

77,505 

118 

109 

8 

82,672 

124 

116 

8K 

87,839 

130 

121 

9 

93,006 

136 

127 

9K 

98,173 

140               132 

10 

103,340 

146               137 

10% 

11% 

111,089 
121,423 

147               145 
148               153 

13 

134,332 

148 

164 

14 

144,666 

154 

172 

15 

155,000 

160 

180 

1% 

160,167 

163 

180 

Q=m(l  - 


0.001     V 


Q'^Q.-Q- 


129 


1 

Temper-     Tempera- 
ature  of       ture  of 
condenser  interior-  of 
water       condenser 
(observed),  (calculat'd) 

Differ- 
ence of 
tempera- 
tures. 

Observations. 

Degrees. 

Degrees. 

Degrees. 

8 



— 

8 

— 

— 

8 

— 

— 

8 

— 

— 

8 
9 

14.1 

—    ( 

The  liquefied 

10 

ie.i 

61^ 

gas  appears. 

12 

18.0 

e!o 

14.5 

20.0 

5.5 

15 

21.7 

6.7 

16 

23.3 

7.3 

17 

25.1 

8.1 

19 

27.4 

8.4 

16  (?) 

30.4 

14.  4(?) 

16  (?) 

32.8 

16.  8(?) 

35 

36.0 

1 

38 

38.0 

0 

38 

40.0 

1 

The  two  following  tables  give  the 
results  of  calculations  for  one  cubic 
meter  of  ammonia  gas,  for  temperatures 
in  the  condenser  ranging  from  +15°  to 
+  40°.  In  the  first  the  temperature  of 


130 

the  interior  of  the  refrigerant  is  taken  at 
-  15°.     In  the  second  table  it  is  -  30°. 

The  numbers  in  the  last  column  are 
calculated  on  the  supposition  that  a  kilo- 
gram of  coal  burned  yields  4000  calories. 

First  case:  $a  =  — 15°,    m=lk.932. 


«H 

o>    . 

02 
.2 

ma 

o 

o  ^ 

O      • 

II 

.  fl 

8 

2  * 

~£  o 

gg 

O    O 

II 

02  a 

0   O 

K!  Q3 

11 

si 

s 
.s| 

tga 

III 

^  o 

PnrO 

*£  ° 

"cS  *"* 

*c  Q 

0   0 

^  .    o 

1«H 

a 

03 

"IrO* 

y 

'I  ^ 

I* 

•M  53 

5  S< 

H    ° 

H 

Q 

& 

Q  o 

H  & 

deg. 

deg. 

cal. 

cal. 

cal. 

cal. 

cal. 

15 

67.77 

638.71 

564.83 

73.88 

7,645 

3<>,580 

20 

81.74 

640.76 

554.49 

86.27 

6,427 

25,708 

25 

95.69 

642.61 

543.98 

98.63 

5,515 

22,060 

30 

109.61 

644.12 

533.29 

110.83 

4,813 

19,252 

35 

123.47 

645.53 

522.43 

123.10 

4,244 

16,976 

40 

137.27 

646.57 

511.31 

135.26 

3,779 

15,116 

131 


Second  case:  /=  —  30°,   ra=lk.023. 


O 

jg  s  i  S  ^ 
5-Si  IrS 


H 


02  g 

O>    O 


Q 


0  2 
<s.5 


18 


deg.    deg.      cal.    ••  cal. 

15  106.07361.77293.04 

20  121.61364.09287.57 

25  1137.13  366. 3 1282. 01 

30  152.61(368.38276 

35  168. 03i370. 31 

40  183.38372.09264 


cal. 
68.73 
76.52 
84.30 

.35   92.03 
270.60J  99.71 

.71107.38 


cal. 
4,263 
3,771 
3,345 
3,003 
2,714 
2,465 


cal. 
17,052 
15,084 
13,380 
12,012 
10,856 
;  9,860 


The  results  indicated  by  the  preceding 
tables  are  large;  they  vary  from  9,860  to 
30,580  negative  calories  for  each  kilo- 
gram of  coal  burned.  We  are  far  from 
attaining  such  results  in  practice. 

We  have  omitted  in  our  calculations  to 
take  into  account  two  conditions  which 
modify  largely  the   theoretical   results: 
1st.  The  necessity  of  cooling  the  ab- 
sorption   chamber    so    that     the 
solution  of  the  gas  may  be  readily 
accomplished. 


132 

2d.  The  influence  of  the  water  carried 
along  with  the  gas. 

We  will  now  examine  the  influence  of 
these  two  causes  of  loss. 

§  37.  When  ammonia  gas  dissolves  in 
water,  considerable  heat  is  disengaged. 

M.  M.  Fabre  and  Silbermann  have  meas- 
ured this  heat  of  solution,  and  found  it 
equal  to  514.cal3  for  each  kilogram  of  gas 
dissolved. 

The  liquid  of  the  absorption  chamber 
being  employed  continually  in  dissolving 
the  gas  from  the  refrigerant,  rises  rapid- 
ly in  temperature,  and  as  the  solubility 
diminishes  with  the  temperature,  it  soon 
reaches  a  condition  at  which  it  ceases  to 
work.  To  insure  successful  working  it 
is  necessary,  therefore,  to  treat  the  ab- 
sorption chamber  to  a  current  of  cold 
water  in  such  a  manner  as  to  maintain  a 
constant  temperature.  We  will  suppose 
this  to  be  the  same  as  that  of  the  con- 
denser £/. 

If  we  denote  by  Q/  the  quantity  of 
heat,  of  which  the  absorption  chamber  is 
relieved,  we  shall  evidently  have 


133 


or 

On  the  other  hand,  the  gas  arriving  at 
the  condenser,  is  always  mixed  with  a 
certain  quantity  of  steam,  usually  about 
6  or  8  per  cent.  By  employing  a  solu- 
tion of  calcium  chloride  instead  of  pure 
water  for  a  solvent,  the  amount  of  watery 
vapor  is  reduced  to  about  three  per  cent. 

The  presence  of  the  steam  reduces  the 
efficiency  to  a  notable  extent.  It  carries 
off  a  portion  of  the  heat  of  the  boiler, 
and,  having  arrived  in  the  refrigerant,  it 
does  not  evaporate,  but,  by  holding  a 
portion  of  the  ammonia,  prevents  it  from 
volatilizing.  It  impedes  the  action  then, 
nearly  in  the  same  way  as  the  waste 
spaces  in  the  mechanical  action  ma- 
chines, but  to  a  greater  extent. 

We  will  proceed  to  determine  the 
influence  of  this  introduction  of  water. 

Let  m,  as  before,  be  the  weight  of  gas 
sent  out  from  the  boiler;  /*  the  weight  of 
water  accompanying  it,  and  the  quantities 
r  and  q  affected  by  the  index  e,  shall  re- 
late to  the  water. 


134 

When  the  mixture  passes  into  the  con- 
denser, the  steam  becomes  liquid,  and 
absorbs  a  certain  weight  m'  of  gas  ;  and 
we  have 

i          (108) 


fi'  being  the  coefficient  of  solubility  by 
volume  of  the  gas  in  water  whose  tem- 

perature is  £/;   —  being  the  weight  of  a 

cubic  meter  of  gas  at  this  temperature. 

According  to  Carius,  the  coefficient  of 
solubility  of  ammonia,  a  gas  in  water,  is 
represented  by  the  empirical  formula 

/?=1049.624-29.4963£  +  0.676873*2 

-0.0095621*'. 

The  quantity  of  heat  Qj  which  will  be 
absorbed  by  the  condenser,  is  equal  to 
the  quantity  of  heat  necessary  to  lower 
the  temperature  of  the  weight  m  of  gas 
from  tl  to  £/,  plus  the  quantity  of  heat 
necessary  to  liquefy  the  weight  m—m' 
of  gas,  plus  the  quantity  of  heat  neces- 
sary to  liquefy,  and  raise  to  the  tempera- 
ture ttf  the  weight  yu  of  steam,  plus  the 


135 

heat  disengaged  by  the  solution  of  the 
weight  m'  of  gas. 
We  shall  have  then 


(qe-qet  +  r^+m's^       (109) 

calling  «/  the  heat  disengaged  by  the 
solution  of  one  kilogram  of  ammonia  gas 
in  water  having  the  temperature  £/. 

The  mixture  passing  into  the  refriger- 
ant, a  certain  quantity  of  the  liquefied 
gas  is  volatilized  until  the  pressure  and 
temperature  become  equal,  respectively, 
to  P2  and  T2,  the  pressure  and  tempera- 
ture of  the  refrigerant.  The  water  will 
retain  in  solution  a  weight  m"  of  gas, 
given  by  the  equation, 


m"  — 


(no) 


02 

The  quantity  of  gas  volatilized  (m-mf) 
is  found  by  the  equation 


The  quantity  of  negative  head  realized 
is 


136 


or 


The  quantity  of  heat  Q/  which  it  is 
necessary  to  supply  to  the  absorption 
chamber  in  order  to  maintain  a  constant 
temperature,  is  equal  to  the  heat  arising 
from  the  solution  of  m—m"  weight  of 
gas,  minus  the  heat  necessary  to  raise 
the  weight  m  of  gas  and  the  weight  JA  of 
water,  from  T2  to  T/. 


The  quantity  of  heat  Q'  which  it  is 
necessary  to  employ  at  the  boiler,  is 
equal  to  Qj  +  Q/—  Q.  We  have  then, 
applying  the  above  values, 

+  (m-mf) 


The  heat  of  solution  s  varies  probably 
with  the  temperature  and  the  pressure  of 


137 

the  gas,  but  we  do  not  know  the  law  of 
this  variation,  and  we,  therefore,  assume 
this  quantity  to  be  constant  and  equal  to 
514.3  calories,  as  found  by  Favre  and 
Silbermann,  for  ordinary  temperatures 
and  pressures. 

Making  s/=s2=  sin  the  above  equation 
it  becomes 


1-^1)  (H5) 
we  have  further 


m= 


0.001 


§  38.  The  two  following  tables  exhibit 
results ;  the  two  cases  of  §  36  are  taken, 
supposing  that  the  weight  of  watery 
vapor  carried  over  is  5  per  cent,  of  the 
weight  of  the  gas  circulating. 


CO 
CO 


o 

II 

2C 


o 

CO 


CO 
J*' 


LO 

rH 

I 


a 
S 


138 


PH  fl  T 

S  1  + 


I" 


M 


^  O  CO 

CQ  oo  -^  os  o 

'•  5O  1C  1O 


O 


TH  00  <M  CO 


'S  00  CO  ^t1  '-'  O5  CO 

OTO  O  O  TH  CQ  CQ  CO 


Oi>CO 
,__;  O  ^  CO  J 


O  1C  J>  O  i-H  GO  J> 
00  t>  J>  CO  ^  CQ 


rrt  ^  CO  "^  CO  £"•  ^ 

^  Cf>  00  00  00  t>  CO 

^  1O  1C  1C  iO  1O  »O 


n^ 
ft 


CO  00  05  O  <M  CO 


^S^oooSco  c 


T)TH  O3  (M  CO  CO  ^ 


139 


O  O5  O  O5  C 
J  CO  i-H  t-l  O5  0 
CO  C 


o. 


* 

M 


^  QO  0 


0  iO  00 

T-H  —  1  i-H  CQ 


Jgl+ 


tq  *  8  * 


io  o 

CO  ^ 


140 

If  we  compare  the  figures  of  these 
tables  with  those  of  §  36,  we  find  that 
the  cooling  of  the  absorption  chamber, 
and  the  presence  of  watery  vapor, 
reduce  the  efficiency  to  a  considerable 
extent. 

We  see  further  that  the  useful  effect 
diminishes  in  proportion  as  the  tempera 
ture  is  lowered  in  the   refrigerant,  but 
that  the  results  remain  the  same  for  the 
same  temperature  of  the  condenser. 

In  the  machines  employing  mechani- 
cal power,  the  efficiency  on  the  other 
hand  diminishes  with  the  temperature  of 
the  refrigerant. 

§  39.  In  the  practical  manufacture  of 
artificial  ice,  we  estimate  the  performance 
at  about  1200  or  1500  negative  calories 
for  each  kilogram  of  coal  burned,  which 
is  about  80  per  cent,  of  the  above  figures. 
The  difference  here  between  theory  and 
practice  may  fairly  be  attributed  to 
external  losses  of  temperature,  to  imper- 
fect action  in  the  exchanges  of  heat,  and 
to  expenditure  of  work  in  driving  the 
pumps. 


141 

The  constructors  of  sulphur  dioxide 
machines  claim  a  practical  result  of  2500 
calories  per  horse  power  per  hour.  As  a 
good  engine  consumes  two  kilograms  of 
coal  per  horse  power  per  hour,  we  are 
afforded  a  means  of  comparing  the  two 
kinds  of  apparatus  in  the  matter  of  econ- 
omy, and  the  result  is  in  favor  of  the 
chemical  action  machines.  The  latter 
also  afford  the  advantage  of  low  temper- 
atures. 

In  the  sulphur  dioxide  machine,  a 
lower  temperature  than— 12°  is  not  at- 
tained without  loss  of  useful  effect,  while 
in  the  ammonia  machine  —25°  and  —30° 
are  readily  and  economically  obtained. 

We  will  not  enter  here  upon  questions 
of  a  purely  practical  character  which 
affect  the  comparative  values  of  the 
several  ice  machines,  as  our  object  has 
been  simply  to  establish  the  theoretic 
conditions  under  which  they  work. 


APPENDIX. 

NOTE  UPON  THE  DETERMINATION  OF  THE 
LATENT  HEAT  OF  VAPORIZATION,  ALSO 
OF  THE  SPECIFIC  HEAT  OF  SULPHUR 
DIOXIDE  AND  AMMONIA  IN  THE  FORM  OF 
LIQUID. 

It  was  shown  in  section  27  that  the 
relation  between  the  pressure,  specific 
volume  and  temperature  of  a  liquefiable 
gas,  being  represented  by  the  equation 

Py=BT-CP",  (116) 

the  constants  B,  C  and  n  can  be  deter- 
mined by    means  of  the   coefficient   of 
dilatation,  and  the  experiments  of  Keg- 
nault  upon  the  compressibility  of  gases. 
These  constants  are 

For  Sulphur  Dioxide.      For  Ammonia. 

B    13.882  52.4943 

C      3.8455          43.7144 
n       0.44487  0.32685 

Eegnault  determined  also  the  elastic 


144 

forces  of  these  substances  at  different 
temperatures,  and  established  the  empir- 
ical formula 


log  F=a 

This  form  not  being  convenient  for 
calculation,  we  have  preferred  to  take  the 
formula  called  Eoche's 


(117) 

and  we  have  calculated  the  three  con- 
stants a,  a  and  m  for  both  sulphur  dioxide 
and  ammonia. 

These  constants  are 

For  Sulphur  Dioxide.  For  Ammonia. 

a=15840  ..........  43474.64 

log.  a=4.1991752  .......  4.6382260 

a=1.04135  .........  1.0386605 

log.  a=  0.0176387  .......  0.0164736 

m=0.0043129  .......  0.0040112 

Finally  M.  Kegnault  found  for  the 
specific  heat  of  sulphur  dioxide  0.15438, 
and  of  ammonia  gas  0.50836. 

On  the  other  hand  Clausius  estab- 
lished between  the  latent  heat  r.  the 


145 

absolute  temperature  T,  the  pressure  P, 
and  the  quantity  u  the  relation 

!L-AT*? 

-  **•*•    ^Ti 

u        .    at 


or  •      r         _M  (118) 

~~ 


u  is  the  increase  of  volume  of  a  unit  of 
weight  of  a  volatile  liquid  when  trans- 
formed into  vapor. 

If  v  is  the   specific    volume  of    the 
vapor,  we  have 

0.001 

$  being  the  density  of  the  liquid,  and 
consequently 

"WLAP     (U9) 


The    constants    B,    C    and  n  being 
known,  the  equation  will  give  APw. 
Knowing  KPu  we  find  r  by  eq.  118. 


146 

or  in  consequence  of  eq.  117 

(120) 


The  equation  120  will  give-r  in  terms 
of  T  and  AFu. 

Finally  it  was  shown  in  §  27  that  the 
quantity  A,  that  is,  the  total  heat  of 
vaporization  satisfies  the  equation 


At  temperature  zero  we  have 

^o  —  ro 

then  it  becomes 

An 

U 


an  equation  in  which  P0  represents  the 
pressure  of  the  vapor  at  zero,  cp  the  spe- 
cific heat  of  the  vapor  at  constant  press- 
ure, and  rQ  the  latent  heat  at  zero. 

The  heat  of  the  liquid 
q=X—  r. 

We  shall  have  then 


(122) 


147 

and  the  specific  heat  of  the  liquid 

C^Tt 

The  equations  (119),  (120),  (121)  and 
(122),  involving  laborious  calculations, 
we  can  replace  the  second  member  by 
empirical  expressions  of  the  formA'+B'tf 
+  CT,  and  then  calculate  the  constants 
by  means  of  three  values  taken  at  the 
two  extremities  and  middle  of  the  ther- 
mometric  scale,  and  previously  deter- 
mined by  aid  of  these  equations. 

We  thus  find  for 

/Sulphur  Dioxide 
APw=8,243  +  0,0196£-0,000116£2 
r=91,396-0,236:U-0,000135Ja 
A  =  91,396  +  0,12723^-0,000131^ 


For  Ammonia 

APw=30,154  +  0,08861^-0,000059^ 
r=313,63-0,6250£-0,002111Z2 
A=313,63  +  0,3808^-0,000282^ 
,001829#2 


148 

The  specific  heat  of  liquid  ammonia  is 
nearly  equal  to  that  of  water.  This  re- 
sult, though  astonishing  at  first,  is 
comprehended  when  we  reflect  that  the 
specific  heat  of  the  gas  at  constant 
pressure  0.50836  is  higher  than  that  of 
steam  (0.4805).  It  would  be  interesting 
to  verify  by  experiment  the  theoretical 
conclusion. 

The  results  obtained  here  for  ammonia 
are,  however,  only  approximate,  for  we 
need,  in  order  to  determine  the  con- 
stants of  eq.  (116),  the  coefficient  of 
dilatation  of  this  gas,  and  at  present  it 
is  not  known. 

To  facilitate  calculations  upon  the  ice 
machines,  we  have  prepared  the  follow- 
ing tables  for  sulphur  dioxide  and  am- 
monia. They  give  for  each  5°  the  heat 
of  the  liquid  <?,  the  total  heat  of  vapori- 
zation A,  the  latent  heat  of  vaporization 
r,  the  internal  latent  heat  p,  the  external 
latent  heat  APu,  and  the  weight  of  a 

cubic  meter  of  vapor  -,  for  the  tempera- 
tures between  —40°  and  +40°. 


149 


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PYNCHON.  INTRODUCTION  TO  CHEMICAL  PHY- 
SICS ;  Designed  for  the  Use  of  Academies, 
Colleges,  and  High  Schools.  Illustrated 
•with  numerous  engravings,  and  containing 
copious  experiments,  with  directions  for 
preparing  them.  By  Thomas  Ruggles  Pyn- 
chon,  D.  D.,  M.  A.,  President  of  Trinity  Col- 
lege, Hartford.  New  edition,  revised  and 
enlarged.  Crown  8vo,  cloth,  .  .  3  00 

PRESCOTT.  CHEMICAL  EXAMINATION  OP  ALCO- 
HOLIC LIQUORS.  A  Manual  of  the  Constit- 
uents of  the  Distilled  Spirits  and  Ferment- 
ed Liquors  of  Commerce,  and  their  Quali- 
tative and  Quantitative  Determinations. 
By  Alb.  B.  Prescott,  Prof,  of  Chemistry, 
University  of  Michigan.  12ino,  cloth,  .  1  50 

ELIOT  AND  STOREFt  A  COMPENDIOUS  MANUAL 
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vised, with  the  co-operation  of  the  Authors, 
toy  William  Ripley  Nichols,  Professor  of 
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D.  VAN  NOSTRAND'S   PUBLICATIONS. 

NAOUET.  LEGAL  CFIEMISTRY.  A  Guide  to  the 
Detection  of  Poisons,  Falsification  of  Writ- 
ings, Adulteration  of  Alimentary  and  Phar- 
maceutical Substances ;  Analysis  of  Ashes, 
and  Examination  of  Hair,  Coins,  Fire-arms 
and  Stains,  as  Applied  to  Chemical  Juris- 
prudence. For  the  Use  of  Chemists,  Phy- 
sicians, Lawyers,  Pharmacists,  and  Ex- 
perts. Translated,  with  additions,  includ- 
ing a  List  of  Boots  and  Memoirs  on  Toxi- 
cology, etc.,  from  the  French  of  A.  Naquet, 
by  J.  P.  Battershall,  Ph.  D. ;  with  a  Preface 
by  C.  F.  Chandler,  PI}.  D.,  M.  D.,  LL.  D. 
Illustrated.  12ino,  cloth,  .  .  .  .  $2  00 

PRESCOTT.  OUTLINES  OF  PROXIMATE  ORGANIC 
ANALYSIS  for  the  Identification,  Separa- 
tion, and  Quantitative  Determination  of 
the  more  commonly  occurring  Organic 
Compounds.  By  Albert  B.  Prescott,  Pro- 
fessor of  Chemistry,  University  of  Michi- 
gan. 12mo,  cloth,  .  .  .  1  75 

TOUGLAS  AND  PRESCOTT.  QUALITATIVE  CHEM- 
ICAL ANALYSIS.  A  Guide  in  the  Practical 
Study  of  Chemistry,  and  in  the  work  of 
Analysis.  By  S.  H.  Douglas  and  A.  B. 
Prescott;  Professors  in  the  University  of 
Michigan.  Second  edition,  revised.  8vo, 
cloth, "...  3  50 

RAMMELSBERG.  GUIDE  TO  A  COURSE  OF 
QUANTITATIVE  CHEMICAL  ANALYSIS,  ESPE- 
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BEILSTEIN.  AN  INTRODUCTION  TO  QUALITATIVE 
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12mo.  cloth, 75 

POPE.  A  Hand-book  for  Electricians  and  Oper- 
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Revised  and  enlarged,  and  fully  illustrat- 

•  ed.    8vo,  cloth,      l 2  00 

9 


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SABINE.  HISTORY  AND  PROGRESS  OF  THE  ELEC- 
TRIC TELEGRAPH,  with  Descriptions  of 
some  of  the  Apparatus.  By  Robert  Sabine, 
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DAVIS  AND  RAE.  HAND  BOOK  OF  ELECTRICAL 
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H.  Davis  and  Frank  B.  Rae.  Illustrated 
with  32  full-page  illustrations.  Second  edi- 
tion. Oblong  8vo,  cloth  extra,  .  .  .  2  00 

HASKINS.  THE  GALVANOMETER,  AND  ITS  USES. 
A  Manual  for  Electricians  and  Students. 
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form,  morocco,  .  .  .  .  .  . '  .  150 

LARRABEE.  CIPHER  AND  SECRET  LETTER  AND 
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GILLMORE  PRACTICAL  TREATISE  ON  LIMES, 
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Brevet  Major-General  U.  S.  Army.  Fifth 
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GILLMORE.  COIGNET  BETON  AND  OTHER  ARTIFI- 
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U.  S.  Engineers,  Brevet  Major-General  U. 
S.  Army.  Nine  plates,  views,  etc.  8vo, 
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GILLMORE.  A  PRACTICAL  TREATISE  ON  THE 
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PAVEMENTS.  By  Q.  A.  Gillmore,  Lt.-Col. 
U.  S.  Engineers,  Brevet  Major-General  U, 
S.  Army.  Seventy  illustrations.  12mo,  do.,  2  00 

GILLMORE.  REPORT  ON  STRENGTH  OF  THE  BUILD- 
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HOLLEY.  AMERICAN  AND  EUROPEAN  RAILWAY 
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HAMILTON.  tlSEFUL  INFORMATION  FOR  RAIL- 
WAY MEN.  Compiled  by  W.  G.  Hamilton, 
Engineer.  Seventh  edition,  revised  and  en- 
larged. 577  pages.  Pocket  form,  morocco, 
gilt, ,  .  $2  00 

STUART.  THE  CIVIL  AND  MILITARY  ENGINEERS 
OF  AMERICA.  By  General  Charles  B. 
Stuart,  Author  of  "  Nav.-il  Dry  Docks  of 
the  United  States,"  etc.,  etc.  With  nine 
linely-executed  Portraits  on  steel,  of  emi- 
nent Engineers,  and  illustrated  by  En- 
gravings of  some  of  the  most  important 
and  original  works  constructed  in  Ameri- 
ca. 8vo,  cloth, 5  00 

ERNST.  A  MANUAL  OF  PRACTICAL  MILITARY 
ENGINEERING.  Prepared  for  the  use  of  the 
Cadets  of  the  U.  S.  Military  Academy, 
and  for  Engineer  Troops.  By  Capt.  O.  H. 
Ernst,  Corps  of  Engineers,  Instructor  in 
Practical  Military  Engineering,  U.  S. 
Military  Academy.  193  wood-cuts  and  3 
lithographed  plates.  12mo,  cloth,  .  .  5  00 

SIMMS.  A  TREATISE  ON  THE  PRINCIPLES  AND 
PRACTICE  OF  LEVELLING,  showing  its  ap- 
plication to  purposes  of  Railway  Engineer- 
ing and  the  Construction  of  Roads,  etc. 
By  Frederick  W.  Simms,  C.  E.  From  the 
fifth  London  edition,  revised  and  correct- 
ed, with  the  addition  of  Mr.  Law's  Prac- 
tical Examples  for  Setting-out  Railway 
Curves.  Illustrated  with  three  lithograph- 
ic plates,  and  numerous  wood-cuts.  8vo, 
cloth,  ....  ...  .  2  50 

JEFFERS.  NAUTICAL  SURVEYING.  By  William 
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ed with  9  copperplates,  and  31  wood-cut 
illustrations.  8vo,  cloth,  .  .  .  .  5  00 

THE  PLANE  TABLE.   ITS  USES  IN  TOPOGRAPHI-         f 
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U.  S.  Coast  Survey.   8vo,  cloth,       .  2  00 

11 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

A  TEXT-BOOK  ON  SURVEYING,  PROJECTIONS, 
AND  PORTABLE  INSTRUMENTS,  for  the  use 
of  the  Cadet  Midshipmen,  at  the  U.  S. 
Naval  Academy.  9  lithographed  plates, 
and  several  wood-cuts.  8vo,  cloth,  .  .  $2  00 

CHAUVENET.  NEW  METHOD  OP  CORRECTING 
LUNAR  DISTANCES.  By  Win.  Chauvenet, 
LL.D.  8vo,  cloth, 2  00 

BURT.  KEY  TO  THE  SOLAR  COMPASS,  and  Sur- 
veyor's Companion;  comprising  all  the 
Rules  necessary  for  use  in  the  Field.  By 
W.  A.  Bui  t,  U.  S.  Deputy  Surveyor.  Sec- 
ond edition.  Pocket-book  form,  tuck,  .  2  50 

HOWARD,  EARTHWORK  MENSURATION  ON  THE 
BASIS  OF  THE  PRISMOIDAL  FORMULAE. 
Containing  simple  and  labor-saving  meth- 
od of  obtaining  Prisnioidal  Contents  direct- 
ly from  End  Areas.  Illustrated  by  Exam- 
ples, and  accompanied  by  Plain  Rules  for 
practical  uses.  By  Con  way  R.  Howard, 
Civil  Engineer,  Richmond,  Va.  Illustrat- 
ed. 8vo,  cloth, 1  50 

MORRIS.  EASY  RULES  FOR  THE  MEASUREMENT 
OF  EARTHWORKS,  by  means  of  the  Pr.is- 
moidal  Formulae.  By  El  wood  Morris, 
Civil  Engineer.  78  illustrations.  8vo,  cloth,  1  50 

CLEVENGER.  A  TREATISE  ON  THE  METHOD  OF 
GOVERNMENT  SURVEYING,  as  prescribed 
by  the  U.  S.  Congress  and  Commissioner  of 
the  General  Land  Office.  With  complete 
Mathematical,  Astronomical,  and  Practi- 
cal Instructions  for  the  use  of  the  U.  S. 
Surveyors,  in  the  Field.  By  S.  V.  Cleven- 
ger,  U.  S.  Deputy  Surveyor.  Illustrated. 
Pocket  form,  morocco,  gilt,  .  .  .  2  50 

HEWSON.  PRINCIPLES  AND  PRACTICE  OF  EM- 
BANKING LANDS  from  River  Floods,  as 
applied  to  the  Levees  of  the  Mississipi. 
By  William  Hewson,  Civil  Engineer.  8vo, 

cloth, 2  00 

12 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

MINIFIE.  A  TEXT-BOOK  OF  GEOMETRICAL 
DRAWING,  for  the  use  of  Mechanics  and 
Schools.  With  Illustrations  for  Drawing 
Plans,  Elevations  of  Buildings  and  Ma- 
chinery. With  over  200  diagrams  on  steel. 
By  William  Miuine,  Architect.  Ninth  edi- 
tion. Royal  8vo,  cloth, $4  00 

MINIFIE  GEOMETRICAL  DRAWING.  Abridged 
from  the  octavo  edit  km,  for  the  use  of 
Schools.  Illustrated  with  48  steel  plates. 
New  edition,  enlarged.  12uio,  cloth,  2  00 

FREE  HAND  DRAWING.  A  G  UIDE  TO  ORNAMEN- 
TAL, Figure,  and  Landscape  Drawing.  By 
an  Art  Student.  Profusely  illustrated. 
I8mo,  boards,  .  ...  50 

AXON.  THE  MECHANIC'S  FRIEND.  A  Collec- 
tion of  Receipts  and  Practical  Suggestions, 
relating  to  Aquaria— Bronzing— Cements 
—Drawing— Dyes— Electricity— Gilding — 
Glass-working—  Glues  —  Horology—  Lac- 
quers—Locomotives —Magnetism  —  Metal- 
working —  Modelling  —  Photography— Py- 
rotechuy— Railways— Solders— Steam  -  En- 
gine—Telegraphy—Taxidermy— Varnishes 
— Waterproofing-and  Miscellaneous  Tools, 
Instruments,  Machines,  and  Processes 
connected  with  the  Chemical  and  Mechan- 
ical Arts.  By  William  E.  Axon,  M.R.S.L. 
12ino,  cloth.  300  illustrations,  .  .  .  1  50 

HARRISON.  MECHANICS'  TOOL  BOOK,  with 
Practical  Rules  and  Suggestions,  for  the 
use  of  Machinists,  Iron  Workers,  and  oth- 
ers. By  W.  B.  Harrison.  44=  illustrations. 
I2nio,  cloth 1  50 

JOYNSON.  THE  MECHANIC'S  AND  STUDENT'S 
GUIDE  in  the  designing  and  Construction 
of  General  Machine  Gearing.  Edited  by 
Francis  H.  Joynson.  With  18  folded 
plates.  8vo,  cloth  .  .  .  2  00 

13 


D.  \AN  NOSTRAND'S  PUBLICATIONS. 

RANDALL.  QUARTZ  OPERATOR'S  HAND-BOOK. 
By  P.  M.  Randall.  New  Edition.  Revised 
and  Enlarged.  Fully  illustrated.  I2mo, 
cloth, $2  00 

LORING.  A  HAND-BOOK  ON  THE  ELECTRO-MAG- 
NETIC TELEGRAPH.  By  A.  E.  Loring.  18mo, 
illustrated.  Paper  boards,  50  cents  ;  cloth,  75 
cents  ;  morocco, 1  OO 

BARNES.  SUBMARINE  WARFARE,  DEFENSIVE 
AND  OFFENSIVE.  Descriptions  of  the  va- 
rious forms  of  Torpedoes,  Submarine  Bat- 
teries and  Torpedo  Boats  actually  used  in 
War.  Methods  of  Ignition  by  Machinery, 
Contact  Fuzes,  and  Electricity,  and  a  full 
account  of  experiments  made  to  deter- 
mine the  Explosive  Force  of  Gunpowder 
under  Water.  Also  a  discussion  of  the  Of- 
fensive Torpedo  system;  its  effect  upon 
Iron-clad  Ship  systems,  and  influence  upon 
future  Naval  Wars.  By  Lieut.-Com.  John 
S.  Barnes,  U.  S.  N.  With  20  lithographic 
plates  and  many  wood-cuts.  8ro,  cloth,  5  00 

FOSTER.  SUBMARINE  BLASTING,  in  Boston 
Harbor,  Mass.  Removal  of  Tower 
and  Corwin  Rocks.  By  John  G.  Foster, 
U.  S.  Eng.  and  Bvt.  Major  General  U.  S. 
Army.  With  seven  Plates.  4to,  cloth,  3  50 

PLYMPTON.  THE  ANEROID  BAROMETER:  Its 
Construction  and  Use,  compiled  from  several 
sources.  16mo,  boards,  illustrated,  50  cents ; 
morocco, 1  OO 

WILLIAMSON.  ON  THE  USE  OF  THE  BAROME- 
TER ON  SURVEYS  AND  RECONNAISSANCES. 
Part  I.-Meteorology  in  its  Connection  with 
Hypsometry.  Part  II.— Barometric  Hyp- 
sometry.  ByR.  S.  Williamson,  Bvt.  Lt.- 
Col.  U.S.A.,  Major  Corps  of  Engineers. 
With  illustrative  tables  and  engravings. 
4to,  cloth, 15  00 


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WILLIAMSON.  PRACTICAL  TABLES  IN  METE- 
OROLOGY  AND  HYPSOMETRY,  in  connection 
with  the  use  of  the  Barometer  By  Col.  R. 
S.  Williamson,  U.  S.  A.  4to,  flexible  cloth,  $2  50 

BUTLER.  PROJECTILES  AND  RIFLED  CANNON 
A  Critical  Discussion  of  the  Principal  Sys 
tems  of  Rifling  and  Projectiles,  with  Prac- 
tical Suggestions  for  their  Improvement. 
By  Capt.  John  S.  Butler,  Ordnance  Corps, 
U.  S.  A.  36  Plates.  4to,  cloth,  .  .  .  7  50 

BENET.  ELECTRO-BALLISTIC  MACHINES,  and 
the  Schultz  Chronoscope.  By  Lt.-Col  8. 
V  Benet,  Chief  of  Ordnance  U.  S.  A. 
Second  edition,  illustrated.  4to,  cloth,  .  3  00 

MICHAELIS.     THE    LE    BOULENGE    CHRONO- 
GRAPH.   ^yith  three  lithographed  folding 
Slates  of  illustrations.    By  Bvt.  Captian 
.  E.  Michaelis,  Ordnance  Corpse,  U.  S.  A. 
4to,  -cloth, 3  00 

NUGENT.  TTEATISE  ON  OPTICS  ;  or  Light  and 
Sight,  theoretically  and  practically  treat- 
ed ;  with  the  application  to  Fine  Art  and 
Industrial  Pursuits.  By  E.  Nugent.  With 
103  illustrations.  12mo,  cloth,  .  .  1  50 

PEIRCE.  SYSTEM  OF  ANALYTIC  MECHANICS.  By- 
Benjamin  Peirce,  Professor  of  Astronomy 
and  Mathematics  in  Harvard  University. 
4to-  cloth,  10  00 

CRAIG.  WEIGHTS  AND  MEASURES.  An  Account 
of  the  Decimal  System,  with  Tables  of  Con- 
version for  Commercial  and  Scientific 
Uses.  By  B.  P.  Craig,  M.  D.  Square  32mo, 
limp  cloth,  .......  50 

ALEXANDER.  UNIVERSAL  DICTIONARY  OF 
WEIGHTS  AND  MEASURES,  Ancient  and 
Modern,  reduced  to  the  standards  of  the 
United  States  of  America.  By  J.  H.  Alex- 
anler.  New  edition.  8 vo,  cloth,  .  .350 
15 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

ELLIOT.  EUROPEAN  LIGHT-HOUSE  SYSTEMS. 
Being  a  Report  of  a  Tour  of  Inspection 
made  in  1873.  By  Major  George  H.  Elliot, 
U.  S.  Engineers.  51  engravings  and  21 
wood-cuts.  8vo,  cloth, $5  00 

SWEET.  SPECIAL  REPORT  ON  COAL.  ByS.  H. 

Sweet.  With  Maps.  8vo,  cloth,  .  .  3  00 

COLBURN.    GAS  WORKS  OF  LONDON.  ByZerah 

Colburn.    12mo,  boards,          ....         60 

WALKER.  NOTES  ON  SCREW  PROPULSION,  its 
Rise  and  History.  By  Capt.  W.  H.  Walker, 
U.S. Navy.  8vo,  cloth,  ....  75 

POOR.  METHOD  OF  PREPARING  THE  LINES  AND 
DRAUGHTING  VESSELS  PROPELLED  BY  SAIL 
OR  STEAM,  including  a  Chapter  on  Laying- 
offon  the  Mould-loft  Floor.  By  Samuel 
M.  Pook,  Naval  Constructor.  Illustrated. 
8vo,  cloth,  .......  5  00 

SAELTZER.  TREATISE  ON  ACOUSTICS  in  connec- 
tion with  Ventilation.  By  Alexander 
Saeltzer.  12mo,  cloth, 2  00 

EASSIE.  A  HAND-BOOK  FOR  THE  USE  OF  CON- 
TACTORS, Builders,  Architects,  Engineers, 
Timber  Merchants,  etc.,  with  information 
for  drawing  up  Designs  and  Estimates. 
250  illustrations.  8vo,  cloth,  .  1  50 

SCHUMANN.  A  MANUAL  OF  HEATING  AND  VEN- 
TILATION IN  ITS  PRACTICAL  APPLICATION 
for  the  use  of  Engineers  and  Architects, 
embracing  a  series  of  Tables  and  Formula 
for  <iimensions  of  heating,  How  and  return 
Pipes  for  steam  and  hot  water  boilers,  flues, 
etc  .  eta  By  P  Schumann,  O.  E.,  U.  S. 
Treasury  Department  12ino.  Illustrated, 
Full  roan, ,.150 

TONER.  DICTIONARY  OF  ELEVATIONS  AND 
CLIMATIC  REGISTER  OF  THE  UNITED  STATES. 
By  J.  M.  Toner,  M  D  8vo.  Paper,  $3.00; 
cloth.  .  .  ,  .  •  3  7§ 

16 


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PLYMPTON.  THE  STAR  FINDER  OR  PLANISPHERE, 
WITH  MOVABLE  HORIZON.  Arranged  by  Prof, 
G.  W,  Plympton,  A.  M.  Printed  in  colors  on 
fine  card-board,  and  in  accordance  with  Proc- 
tor's Star  Atlas,  $1  00 

CALDWELL  &  BRENEMAN.  MANUAL  OP  INTRO- 
DUCTORY CHEMICAL  PRACTICE,  for  the  use  of 
Students  in  Colleges  and  Normal  and  High 
Schools.  By  Prof.  George  C.  Caldwell,  and  A. 
A.  Breneman,  of  Cornell  University.  Second 
edition,  revised  and  corrected.  8vo,  cloth,  il- 
lustrated. New  and  enlarged  edition,  .  .150 

SCOFFERN,  TRURAN,  Etc.  THE  USEFUL  METALS 
AND  THEIR  ALLOYS,  employed  in  the  conver- 
sion of  Iron,  Copper,  Tin,  Zinc,  Antimony, and 
Lead  ores,  with  their  applications  to  the  In- 
dustrial Arts.  By  John  Scoffern,  William  Tru- 
ran,  etc.  Fifth  edition,  8vo,  half-calf,  .  ,375 

ROSE.  THE  PATTERN  MAKER'S  ASSISTANT,  em- 
bra  cing  Lathe  Work,  Branch  Work,  Core  Work, 
Sweep  Work,and  Practical  Gear  Constructions, 
the  Preparation  and  Use  of  Tools,  together 
with  a  large  collection  of  useful  and  valuable 
Tables.  By  Joshua  Rose,  M.E,  Illustrated 
with  250  engravings,  8 vo,  cloth,  ,  ,  ,250 

SCRIBNER.  ENGINEERS'  AND  MECHANICS'  COM- 
PANION, comprising  United  States  Weights 
and  Measures  ;  Mensuration  of  Superfices  and 
Solids ;  Tables  of  Squares  and  Cubes  ;  Square 
and  Cube  Roots  ;  Circumference  and  Areas  of 
Circles;  the  Mechanical  Powers;  Centers  of 
Gravity  ;  Gravitation  of  Bodies  ;  Pendulums ; 
Specific  Gravity  of  Bodies  ;  Strength,  Weight, 
and  Crush  of  Materials  ;  Water  Wheels  ;  Hy- 
drostatics ;  Hydraulics ;  Statics  ;  Centers  of 
Percussion  and  Gyration  ;  Friction  Heat ;  Ta- 
bles of  the  Weight  of  Metals  ;  Scantling,  etc. ; 
Steam  and  the  Steam  Engine.  By  J.  M.  Scrib- 
ner,  A,  M.  18th  ed.  revised,  16mo,  full  morocco,  1  50 
17 


D.  VAN  NOSTRAND'S  NRW  PUBLICATIONS. 

SCRIBNER.   ENGINEERS',  CONTRACTORS'  AND  SUR- 
VEYORS' POCKET   TABLE-BOOK  :    Comprising 
Logarithms  of  Numbers,  Logarithmic  Signs 
and  Tangents,  Natural  Signs  and  Natural  Tan- 
gents, the  Traverse  Table,  and  a  full  and  com- 
glete  set  of  Excavation  and  Embankment  Ta- 
les, together  with  numerous  other  valuable 
tables  for  Engineers,  etc.    By  T.  M,  Scribner, 
A.M.    10th  ed.  revised,  16mo,  full  morocco,   $1  50 

EDDY.  RESEARCHES  IN  GRAPHICAL  STATICS, 
embracing  New  Constructions  in  Graphical 
Statics,  a  new  General  Method  in  Graphical 
Statics,  and  the  Theory  of  Internal  Stress  in 
Graphical  Statics.  By  Prof.  Henry  T.  Eddy, 
of  the  University  of  Cincinnati.  8vo,  cloth,  ,  1  50 

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XXVII.  ON  BOILER  INCRUSTATION  AND  CORROSION. 
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XXVIII.  ON  TRANSMISSION  OF  POWER  BY  WIRE  ROPE. 
By  Albert  W.  Stahl. 

XXIX.  INJECTORS  ;  their  Theory  and  Use.     Trans- 
lated from  the  French  of  M.  Leon  Pouchet. 

XXX.  TERRESTRIAL  MAGNETISM  AND  THE  MAGNETISM 
OF  IRON  VESSELS.    By  Prof.  Fairruan  Rogers. 

XXXI.  THE   SANITARY    CONDITION   OF  DWELLING 
HOUSES  IN  TOWN  AND  COUNTRY.    By  George  E. 
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Agricultural  Works.    Illustrated. 

XXXII.  CABLE  MAKING  FOR  SUSPENSION  BRIDGES, 
as  exemplified  in  the  Construction  of  the  East 
River  Bridge.    By  Wilhelin  Hildenbrand,  C.  E. 

XXXIII.  MECHANICS   OP  VENTILATION.      By    George 
W.  Rafter,  Civil  Engineer. 

XXXIV.  FOUNDATIONS.    By  Prof.  Jules  Gaudard,  C. 
E.    Translated  from  the  French,  by  L.  F.  Vernon 
Harcourt,  M.  I.  C.  E. 

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AND  USE.  Compiled  by  Professor  George  W.  Plymp- 
ton.    Illustrated. 

XXXVI.  MATTER  AND  MOTION.      By  J.  Clerk  Maxwell, 
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ods and  Kesults.    By  Frank  De  Yeaux  Carpenter, 
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